H. Stefancic: The Accelerated Expansion of the Universe and the Cosmological Constant Problem
85
The accelerated expansion of the universe and the cosmological constant problem Spring Summer School on Strings Cosmology and Particles 31 March – 4 April 2009, Belgrade-Niš, Serbia Hrvoje Štefančić, Theoretical Physics Division, Ruđer Bošković Institute, Zagreb, Croatia
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Transcript of H. Stefancic: The Accelerated Expansion of the Universe and the Cosmological Constant Problem
The accelerated expansion of the universe and the cosmological
constant problem
Spring Summer School on Strings Cosmology and Particles
31 March ndash 4 April 2009 Belgrade-Niš Serbia
Hrvoje Štefančić Theoretical Physics Division
Ruđer Bošković Institute Zagreb Croatia
Big issues - observational and theoretical
bull Present accelerated expansion of the universe ndash observational discovery
bull The cosmological constant (vacuum energy) problem ndash theoretical challenge
Our concept of the (present) universe
bull Evolution dominated by gravity ndash the interactions governing the evolution of the
universe have to have long range to be effective at cosmological distances
ndash matter is neutral at cosmological (and much smaller) scales
bull General relativity bull Known forms of matter (radiation nonrelativistic
matter)bull Four dimensional universe
The observed universe
bull Isotropic (CMB averaged galaxy distribution at scales gt 50-100 Mpc)
bull Homogeneous ndash less evidence (indirect) ndash Copernican principle
bull Homogeneous and isotropic ndash Cosmological principle
bull Robertson-Walker metric
Expansion of the universe
bull Hubble (1929) ndash dynamical universe bull Cosmological redshiftbull Standard forms of matter lead to decelerated
expansion
bull Inflation ndash early epoch of the accelerated expansion
bull 1998 ndash universe accelerated (decelerated universe expected)
FRW model ndash theoretical description of the expansion
bull Contents cosmic fluids (general EOS)
bull General relativity in 4D
bull Friedmann equation
bull Continuity equation (Bianchi identity - covariant conservation of energy-momentum tensor)
bull Acceleration
FRW model
bull Critical density
bull Omega parameters
bull Cosmic sum rules
Cosmological observations ndash mapping the expansion
bull Standard candles (luminosity distance)bull Supernovae Ia GRB
bull Standard rulersbull CMB (cosmic microwave background)bull BAO (baryonic acoustic oscillations)
bull Others (gravitational lensing)
Supernovae of the type Ia
bull Standard candles ndash known luminositybull Binary stars ndash physics of SNIa understood bull Light curve fittingbull Luminosity distance ndash can be determined both
observationally and theoretically
bull SNIa dimming ndash signal of the accelerated expansion
Cosmological observations - SNIa httpimaginegsfcnasagovdocsscienceknow_l2supernovaehtml
httpwwwastrouiucedu~pmrickerresearchtype1a
Cosmological observations - CMB
httpmapgsfcnasagov
Cosmological observations - LSS
structure at cosmological scales (LSS)
httpcassdssorgdr5entoolsplaces
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
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- Slide 31
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- Slide 33
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- Slide 38
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- Slide 40
- Slide 41
- Slide 42
- Slide 43
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- Slide 46
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- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
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- Slide 60
- Slide 61
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- Slide 66
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- Slide 71
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- Slide 73
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- Slide 75
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- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Big issues - observational and theoretical
bull Present accelerated expansion of the universe ndash observational discovery
bull The cosmological constant (vacuum energy) problem ndash theoretical challenge
Our concept of the (present) universe
bull Evolution dominated by gravity ndash the interactions governing the evolution of the
universe have to have long range to be effective at cosmological distances
ndash matter is neutral at cosmological (and much smaller) scales
bull General relativity bull Known forms of matter (radiation nonrelativistic
matter)bull Four dimensional universe
The observed universe
bull Isotropic (CMB averaged galaxy distribution at scales gt 50-100 Mpc)
bull Homogeneous ndash less evidence (indirect) ndash Copernican principle
bull Homogeneous and isotropic ndash Cosmological principle
bull Robertson-Walker metric
Expansion of the universe
bull Hubble (1929) ndash dynamical universe bull Cosmological redshiftbull Standard forms of matter lead to decelerated
expansion
bull Inflation ndash early epoch of the accelerated expansion
bull 1998 ndash universe accelerated (decelerated universe expected)
FRW model ndash theoretical description of the expansion
bull Contents cosmic fluids (general EOS)
bull General relativity in 4D
bull Friedmann equation
bull Continuity equation (Bianchi identity - covariant conservation of energy-momentum tensor)
bull Acceleration
FRW model
bull Critical density
bull Omega parameters
bull Cosmic sum rules
Cosmological observations ndash mapping the expansion
bull Standard candles (luminosity distance)bull Supernovae Ia GRB
bull Standard rulersbull CMB (cosmic microwave background)bull BAO (baryonic acoustic oscillations)
bull Others (gravitational lensing)
Supernovae of the type Ia
bull Standard candles ndash known luminositybull Binary stars ndash physics of SNIa understood bull Light curve fittingbull Luminosity distance ndash can be determined both
observationally and theoretically
bull SNIa dimming ndash signal of the accelerated expansion
Cosmological observations - SNIa httpimaginegsfcnasagovdocsscienceknow_l2supernovaehtml
httpwwwastrouiucedu~pmrickerresearchtype1a
Cosmological observations - CMB
httpmapgsfcnasagov
Cosmological observations - LSS
structure at cosmological scales (LSS)
httpcassdssorgdr5entoolsplaces
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
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- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Our concept of the (present) universe
bull Evolution dominated by gravity ndash the interactions governing the evolution of the
universe have to have long range to be effective at cosmological distances
ndash matter is neutral at cosmological (and much smaller) scales
bull General relativity bull Known forms of matter (radiation nonrelativistic
matter)bull Four dimensional universe
The observed universe
bull Isotropic (CMB averaged galaxy distribution at scales gt 50-100 Mpc)
bull Homogeneous ndash less evidence (indirect) ndash Copernican principle
bull Homogeneous and isotropic ndash Cosmological principle
bull Robertson-Walker metric
Expansion of the universe
bull Hubble (1929) ndash dynamical universe bull Cosmological redshiftbull Standard forms of matter lead to decelerated
expansion
bull Inflation ndash early epoch of the accelerated expansion
bull 1998 ndash universe accelerated (decelerated universe expected)
FRW model ndash theoretical description of the expansion
bull Contents cosmic fluids (general EOS)
bull General relativity in 4D
bull Friedmann equation
bull Continuity equation (Bianchi identity - covariant conservation of energy-momentum tensor)
bull Acceleration
FRW model
bull Critical density
bull Omega parameters
bull Cosmic sum rules
Cosmological observations ndash mapping the expansion
bull Standard candles (luminosity distance)bull Supernovae Ia GRB
bull Standard rulersbull CMB (cosmic microwave background)bull BAO (baryonic acoustic oscillations)
bull Others (gravitational lensing)
Supernovae of the type Ia
bull Standard candles ndash known luminositybull Binary stars ndash physics of SNIa understood bull Light curve fittingbull Luminosity distance ndash can be determined both
observationally and theoretically
bull SNIa dimming ndash signal of the accelerated expansion
Cosmological observations - SNIa httpimaginegsfcnasagovdocsscienceknow_l2supernovaehtml
httpwwwastrouiucedu~pmrickerresearchtype1a
Cosmological observations - CMB
httpmapgsfcnasagov
Cosmological observations - LSS
structure at cosmological scales (LSS)
httpcassdssorgdr5entoolsplaces
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
The observed universe
bull Isotropic (CMB averaged galaxy distribution at scales gt 50-100 Mpc)
bull Homogeneous ndash less evidence (indirect) ndash Copernican principle
bull Homogeneous and isotropic ndash Cosmological principle
bull Robertson-Walker metric
Expansion of the universe
bull Hubble (1929) ndash dynamical universe bull Cosmological redshiftbull Standard forms of matter lead to decelerated
expansion
bull Inflation ndash early epoch of the accelerated expansion
bull 1998 ndash universe accelerated (decelerated universe expected)
FRW model ndash theoretical description of the expansion
bull Contents cosmic fluids (general EOS)
bull General relativity in 4D
bull Friedmann equation
bull Continuity equation (Bianchi identity - covariant conservation of energy-momentum tensor)
bull Acceleration
FRW model
bull Critical density
bull Omega parameters
bull Cosmic sum rules
Cosmological observations ndash mapping the expansion
bull Standard candles (luminosity distance)bull Supernovae Ia GRB
bull Standard rulersbull CMB (cosmic microwave background)bull BAO (baryonic acoustic oscillations)
bull Others (gravitational lensing)
Supernovae of the type Ia
bull Standard candles ndash known luminositybull Binary stars ndash physics of SNIa understood bull Light curve fittingbull Luminosity distance ndash can be determined both
observationally and theoretically
bull SNIa dimming ndash signal of the accelerated expansion
Cosmological observations - SNIa httpimaginegsfcnasagovdocsscienceknow_l2supernovaehtml
httpwwwastrouiucedu~pmrickerresearchtype1a
Cosmological observations - CMB
httpmapgsfcnasagov
Cosmological observations - LSS
structure at cosmological scales (LSS)
httpcassdssorgdr5entoolsplaces
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Expansion of the universe
bull Hubble (1929) ndash dynamical universe bull Cosmological redshiftbull Standard forms of matter lead to decelerated
expansion
bull Inflation ndash early epoch of the accelerated expansion
bull 1998 ndash universe accelerated (decelerated universe expected)
FRW model ndash theoretical description of the expansion
bull Contents cosmic fluids (general EOS)
bull General relativity in 4D
bull Friedmann equation
bull Continuity equation (Bianchi identity - covariant conservation of energy-momentum tensor)
bull Acceleration
FRW model
bull Critical density
bull Omega parameters
bull Cosmic sum rules
Cosmological observations ndash mapping the expansion
bull Standard candles (luminosity distance)bull Supernovae Ia GRB
bull Standard rulersbull CMB (cosmic microwave background)bull BAO (baryonic acoustic oscillations)
bull Others (gravitational lensing)
Supernovae of the type Ia
bull Standard candles ndash known luminositybull Binary stars ndash physics of SNIa understood bull Light curve fittingbull Luminosity distance ndash can be determined both
observationally and theoretically
bull SNIa dimming ndash signal of the accelerated expansion
Cosmological observations - SNIa httpimaginegsfcnasagovdocsscienceknow_l2supernovaehtml
httpwwwastrouiucedu~pmrickerresearchtype1a
Cosmological observations - CMB
httpmapgsfcnasagov
Cosmological observations - LSS
structure at cosmological scales (LSS)
httpcassdssorgdr5entoolsplaces
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
FRW model ndash theoretical description of the expansion
bull Contents cosmic fluids (general EOS)
bull General relativity in 4D
bull Friedmann equation
bull Continuity equation (Bianchi identity - covariant conservation of energy-momentum tensor)
bull Acceleration
FRW model
bull Critical density
bull Omega parameters
bull Cosmic sum rules
Cosmological observations ndash mapping the expansion
bull Standard candles (luminosity distance)bull Supernovae Ia GRB
bull Standard rulersbull CMB (cosmic microwave background)bull BAO (baryonic acoustic oscillations)
bull Others (gravitational lensing)
Supernovae of the type Ia
bull Standard candles ndash known luminositybull Binary stars ndash physics of SNIa understood bull Light curve fittingbull Luminosity distance ndash can be determined both
observationally and theoretically
bull SNIa dimming ndash signal of the accelerated expansion
Cosmological observations - SNIa httpimaginegsfcnasagovdocsscienceknow_l2supernovaehtml
httpwwwastrouiucedu~pmrickerresearchtype1a
Cosmological observations - CMB
httpmapgsfcnasagov
Cosmological observations - LSS
structure at cosmological scales (LSS)
httpcassdssorgdr5entoolsplaces
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
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- Slide 24
- Slide 25
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- Slide 31
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- Slide 33
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- Slide 35
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- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
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- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
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- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
FRW model
bull Critical density
bull Omega parameters
bull Cosmic sum rules
Cosmological observations ndash mapping the expansion
bull Standard candles (luminosity distance)bull Supernovae Ia GRB
bull Standard rulersbull CMB (cosmic microwave background)bull BAO (baryonic acoustic oscillations)
bull Others (gravitational lensing)
Supernovae of the type Ia
bull Standard candles ndash known luminositybull Binary stars ndash physics of SNIa understood bull Light curve fittingbull Luminosity distance ndash can be determined both
observationally and theoretically
bull SNIa dimming ndash signal of the accelerated expansion
Cosmological observations - SNIa httpimaginegsfcnasagovdocsscienceknow_l2supernovaehtml
httpwwwastrouiucedu~pmrickerresearchtype1a
Cosmological observations - CMB
httpmapgsfcnasagov
Cosmological observations - LSS
structure at cosmological scales (LSS)
httpcassdssorgdr5entoolsplaces
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
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- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Cosmological observations ndash mapping the expansion
bull Standard candles (luminosity distance)bull Supernovae Ia GRB
bull Standard rulersbull CMB (cosmic microwave background)bull BAO (baryonic acoustic oscillations)
bull Others (gravitational lensing)
Supernovae of the type Ia
bull Standard candles ndash known luminositybull Binary stars ndash physics of SNIa understood bull Light curve fittingbull Luminosity distance ndash can be determined both
observationally and theoretically
bull SNIa dimming ndash signal of the accelerated expansion
Cosmological observations - SNIa httpimaginegsfcnasagovdocsscienceknow_l2supernovaehtml
httpwwwastrouiucedu~pmrickerresearchtype1a
Cosmological observations - CMB
httpmapgsfcnasagov
Cosmological observations - LSS
structure at cosmological scales (LSS)
httpcassdssorgdr5entoolsplaces
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Supernovae of the type Ia
bull Standard candles ndash known luminositybull Binary stars ndash physics of SNIa understood bull Light curve fittingbull Luminosity distance ndash can be determined both
observationally and theoretically
bull SNIa dimming ndash signal of the accelerated expansion
Cosmological observations - SNIa httpimaginegsfcnasagovdocsscienceknow_l2supernovaehtml
httpwwwastrouiucedu~pmrickerresearchtype1a
Cosmological observations - CMB
httpmapgsfcnasagov
Cosmological observations - LSS
structure at cosmological scales (LSS)
httpcassdssorgdr5entoolsplaces
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Cosmological observations - SNIa httpimaginegsfcnasagovdocsscienceknow_l2supernovaehtml
httpwwwastrouiucedu~pmrickerresearchtype1a
Cosmological observations - CMB
httpmapgsfcnasagov
Cosmological observations - LSS
structure at cosmological scales (LSS)
httpcassdssorgdr5entoolsplaces
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Cosmological observations - CMB
httpmapgsfcnasagov
Cosmological observations - LSS
structure at cosmological scales (LSS)
httpcassdssorgdr5entoolsplaces
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Cosmological observations - LSS
structure at cosmological scales (LSS)
httpcassdssorgdr5entoolsplaces
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Standard cosmological model (up to 1998)
bull Destiny determined by geometry
bull Interplay of spatial curvature and matter content (Ω
m + Ω
k=1)
bull Even EdS model advocated (Ωm=1)
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Spatial curvature
bull COBE ndash spatial curvature is small
bull EdS must do the job (models with considerable Ω
k are ruled out by the
observation of CMB temperature anisotropies
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
SNIa observations (1998)
bull Observations by two teamsndash High z SN Search Team Riess et al
httpcfa-wwwharvardedusupernovahomehtmlndash Supernova Cosmology Project Perlmutter et al
httpsupernovalblgov
bull ΛCDM model ndash fits the data very well
bull Measurement in the redshift range where the expansion of the universe is really accelerated or there is the transition from decelerated to accelerated expansion ndash ldquodirect measurementrdquo
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
CMB and BAO
bull Influence to the determination of the acceleration ndash indirectly
bull CMB ndash mainly through the distance to the surface of last scattering
bull BAO ndash similarly
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Combining observational data
bull Degeneracies of cosmic parameters - different combinations of cosmic parameters may produce the same observed phenomena
bull Removal of degeneracies ndash using different observations at different redshifts (redshift intervals)
bull SNIa + WMAP + BAO ndash precision cosmology
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
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- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
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- Slide 65
- Slide 66
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- Slide 68
- Slide 69
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- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Observational constraints to the DE EOS
E Komatsu et al Five-Year Wilkinson Microwave Anisotropy
Probe (WMAP) Observations Cosmological Interpretation
httparxivorgabs08030547
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Accelerated expansion
bull In a FRW universe the observed signals strongly favor a presently accelerated expansion of the universe (and reject EdS model)
bull Do we interpret the observational data correctly
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
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- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Classification of theoretical
approaches ll
R Bean S Caroll M Trodden Insights into dark energy interplay between theory and observation
Rachel Bean (Cornell U Astron Dept) Sean M Carroll (Chicago U EFI amp KICP Chicago) Mark Trodden (Syracuse U) Oct 2005 5pp
White paper submitted to Dark Energy Task Force
httparxivorgabsastro-ph0510059
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Distorted signals and unjustified assumptions
bull Photons from SNIa convert to axions in the intergalactic magnetic field ndash light signal dissipated ndash Reduction in intensity confused for the effects of
acceleration
bull C Csaki N Kaloper J Terning Phys Rev Lett 88 (2002) 161302ndash does not work (very interesting attempt ndash
invokes more or less standard (or at least already known physics)
ndash connection with the phantom ldquomiragerdquo
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Distorted signals and unjustified assumptions
bull The influence of inhomogeneities (below 50-100 Mpc)bull Nonlinearity of GR in its fundamental formbull Solving Einstein equations in an inhomogeneous
universe and averaging the solutions is not equivalent to averaging sources and solving Einsteins equations in a homogeneous universe
bull No additional components (just NR matter)bull The acceleration is apparent bull The perceived acceleration begins with the onset of
structure formation ndash very convenient for the cosmic coincidence problem
bull The effect is not sufficient to account for acceleration but is should be taken into considerations in precise determination of cosmic parameters
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Distorted signals and unjustified assumptions
bull Inhomogeneities at scales above the Hubble horizon
bull Underdense regionbull Relinquishing the Copernican principle
bull Falsifiability
bull No additional components
bull The effect of ldquosuper large scale structurerdquo
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Mechanism of the acceleration
bull No acceleration in the ldquoold standard cosmological modelrdquo
bull Our (pre)concepts of the universe have to be modifiedndash Modifying contents ndash dark energy (+ DM)
ndash Modyfing gravity ndash modified (dark) gravityndash Modifying dimensionality ndash new (large) dimesions ndash
braneworld modelsndash ndash and combinations
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
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- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Dark energy
bull Acceleration by adding a new component ndash a dark energy component
bull Key property ndash sufficiently negative pressure
bull Physical realization of a negative pressurendash Geometric effect (Lambda from the left side of Einstein eq)ndash Dynamics of scalar field - domination of potential energy
over kinetic energy
ndash Corpuscular interpretation ndash unusual dispersion relation ndash energy decreasing with the size of momentum
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Dark energy
bull DE equation of state
bull Dynamics of ρd in terms of a
ndash w gt -1 quintessencendash w = -1 cosmological termndash w lt -1 phantom energy
bull Multiple DE components
bull Crossing of the cosmological constant barrier
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
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- Slide 31
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- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
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- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Dark sector
bull DE interacting with other cosmic components
bull Interaction with dark matter
bull Unification of dark matter and dark energy
bull Chaplygin gas ndash EOS
ndash scaling with a
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
DE models
bull Cosmic fluid
bull Scalar fields (quintessence phantom)
bull
bull Effective description of other acceleration mechanisms (at least at the level of global expansion)
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
ΛCDM
bull Benchmark model
bull Only known concepts (CC NR matter radiation)
bull small number of parameters
bull The size of Λ not understood ndash cosmological constant problem(s)
bull Problems with ΛCDM cosmology
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Quintessence
bull Dynamics of a scalar field in a potential
bull Freezing vs thawing models
bull ldquotracker fieldrdquo models
bull k-essence (noncanonical kinetic terms)
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Phantom energy
bull Energy density growing with time
bull Big rip
bull Stabilitybull Problems with microscopic formulation
bull Instability to formation of gradients
bull Effective description
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Singularities
bull New types of singularities
bull Finite time (finite scale factor) singularities
bull Sudden singularities
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Modified gravity
bull Modification of gravity at cosmological scales
bull Dark gravity (effective dark energy)bull F(R) gravity ndash various formulations (metric
Palatini metric-affine)
bull Conditions for stability
bull Stringent precision tests in Solar system and astrophysical systems
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Braneworlds
bull Matter confined to a 4D branebull Gravity also exists in the bulkbull Dvali-Gabadadaze-Poratti (DGP)
bull Different DGP models ndash discussion of the status
bull Phenomenological modifications of the Friedmann equation ndash Cardassian expansion
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
The cosmological constant
bull Formally allowed ndash a part of geometry bull Introduced by Einstein in 1917 ndash a needed element
for a static universe
bull Pauli ndash first diagnosis of a problem with zero point energies
bull Identification with vacuum energy ndash Zeldovich 1967bull Frequently used ldquopatchrdquo
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
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- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
The expansion with the
cosmological constant
J Solagrave hep-ph0101134v2
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
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- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
The expansion with the cosmological constant
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
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- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Contributions to vacuum energy
bull Zero point energies ndash radiative correctionsndash Bosonicndash Fermionic
bull Condensates ndash classical contributionsndash Higgs condensatendash QCD condensates
ndash
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 13
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- Slide 16
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- Slide 21
- Slide 22
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- Slide 40
- Slide 41
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- Slide 45
- Slide 46
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- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
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- Slide 73
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- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Zero point energies
bull QFT estimatesndash real scalar field
ndash spin j
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
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- Slide 31
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- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
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- Slide 44
- Slide 45
- Slide 46
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- Slide 49
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- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
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- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Condensates
bull Phase transitions leave contributions to the vacuum energy
bull Higgs potential
bull minimum at
bull contribution to vacuum energy
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
- Slide 48
- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
- Slide 62
- Slide 63
- Slide 64
- Slide 65
- Slide 66
- Slide 67
- Slide 68
- Slide 69
- Slide 70
- Slide 71
- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
The size of the CC
bull Many disparate contributions
bull Virtually all many orders of magnitude larger than the observed value
bull ZPE - Planck scale ldquocutoffrdquo asymp 1074 GeV4
bull ZPE - TeV scale ldquocutoffrdquo asymp 1057 GeV4
bull ZPE - ΛQCD
scale ldquocutoffrdquo asymp 10-5 GeV4
bull Higgs condensate asymp -108 GeV4
bull melectron
4 asymp 10-14 GeV4
bull The observed value
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 20
- Slide 21
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- Slide 40
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- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
The ldquooldrdquo cosmological constant problem ndash the problem of size
bull Discrepancy by many orders of magnitude (first noticed by Pauli for the ZPE of the electromagnetic field)
bull Huge fine-tuning impliedbull How huge and of which nature
ndash Numerical example 10120
1-0999999999999999999999999999999999999999999999999999
999999999999999999999999999999999999999999999999999999999999999999999
=00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000001
ndash Financial example
Instability to variation of a single contribution (parameter)
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
The ldquooldrdquo cosmological constant problem
bull Fundamental theoretical problem ndash the problem of the vacuum energy density
bull All proposed solutions assume that the ldquooldrdquo CC problem is somehow solvedndash ΛCDM model ndash CC relaxed to the observed valuendash DE models and other models ndash CC is zero or much smaller in
absolute value compared to the observed DE energy density
bull Even should the future observations confirm the dynamical nature of DE or some other alternative acceleration mechanism the ldquooldrdquo CC problem must be resolved
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
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- Slide 25
- Slide 26
- Slide 27
- Slide 28
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- Slide 31
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- Slide 33
- Slide 34
- Slide 35
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- Slide 37
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- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
- Slide 45
- Slide 46
- Slide 47
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- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
- Slide 59
- Slide 60
- Slide 61
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- Slide 65
- Slide 66
- Slide 67
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- Slide 69
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- Slide 73
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- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
DE vs CC
bull Raphael Bousso ldquoTASI lectures on the cosmological constantrdquondash ldquoIf a poet sees something that walks like a duck
and swims like a duck and quacks like a duck we will forgive him for entertaining more fanciful possibilities It could be a unicorn in a duck suit ndash whos to say But we know that more likely its a duckrdquo
bull Conditions for a mechanism solving the CC problem
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
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- Slide 22
- Slide 23
- Slide 24
- Slide 25
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- Slide 83
- Slide 84
- Slide 85
-
Proposed solutions of the ldquooldrdquo CC problem
bull Classification (closely following S Nobbenhuis gr-qc0609011)ndash Symmetryndash Back-reaction mechanismsndash Violation of the equivalence principlendash Statistical approaches
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
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- Slide 16
- Slide 17
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- Slide 20
- Slide 21
- Slide 22
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- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
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- Slide 31
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- Slide 33
- Slide 34
- Slide 35
- Slide 36
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- Slide 38
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- Slide 40
- Slide 41
- Slide 42
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- Slide 44
- Slide 45
- Slide 46
- Slide 47
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- Slide 49
- Slide 50
- Slide 51
- Slide 52
- Slide 53
- Slide 54
- Slide 55
- Slide 56
- Slide 57
- Slide 58
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- Slide 69
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- Slide 73
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- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Symmetry
bull Supersymmetry
bull Scale invariance
bull Conformal symmetrybull Imaginary space
bull Energy rarr - Energy
bull Antipodal symmetry
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
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- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Back-reaction mechanisms
bull Scalar
bull Gravitons
bull Running CC from Renormalization groupbull Screening caused by trace anomaly
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
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- Slide 21
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- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
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- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Violation of the equivalence principle
bull Non-local Gravity Massive gravitons
bull Ghost condensation
bull Fat gravitonsbull Composite gravitons as Goldstone bosons
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
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- Slide 72
- Slide 73
- Slide 74
- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Statistical approaches
bull Hawking statistics
bull Wormholes
bull Anthropic Principle
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
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- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
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- Slide 44
- Slide 45
- Slide 46
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- Slide 49
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- Slide 51
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- Slide 53
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- Slide 73
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- Slide 75
- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
The cosmic coincidence problem ndash the problem of timing
bull Why the CC (DE) energy density and the energy density of (NR) matter are comparable (of the same order of magnitude) at the present epoch
bull A problem in a DE (CC) approach to the problem of accelerated expansionndash DE (CC) energy density scale very differently with the
expansion (if presently comparable they were very different in the past and will be very different in the future
bull NR ρ ~ a-3
bull DE ρ ~ a-3(1+w) slower than a-2 CC ~ 1
bull Also present in many approaches not based on DE
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
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- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
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- Slide 33
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- Slide 40
- Slide 41
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- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Possible solutions of the cosmic coincidence problem
bull Naturally solved in (matter) back-reaction approaches
bull ldquotracker fieldrdquobull Oscillating DE model
bull DE-DM interaction models (although problem still present in eg Chaplygin gas model)
bull Composite DE model (LambdaXCDM model)ndash Two interacting DE components a (dynamical)
cosmological term and an additional DE component (cosmon X)
bull hellip
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
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- Slide 33
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- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Composite dark energy ndash ΛXCDM models
ordinary matter (radiation and NR matter) separately conserved)
ΛXCDM11 CT interacting with cosmon
minus J Grande J Solagrave H Š JCAP 0608 (2006) 011
ΛXCDM2 varaible CT i G X concerved
minus J Grande J Solagrave H Š Phys Lett B645 (2007) 236
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
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- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Ratio of DE and matter energy density
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
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- Slide 27
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- Slide 29
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- Slide 31
- Slide 32
- Slide 33
- Slide 34
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- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
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- Slide 44
- Slide 45
- Slide 46
- Slide 47
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- Slide 49
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- Slide 51
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- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Parameter constraints primordial nucelosynthesis
Existence of a stopping point
height of the maximum of r
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 14
- Slide 15
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- Slide 27
- Slide 28
- Slide 29
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- Slide 31
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- Slide 73
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- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Parameter constraints ndash cross sections
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 13
- Slide 14
- Slide 15
- Slide 16
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- Slide 20
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- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
The CC relaxation mechansim
bull Two component model (HŠ PhysLett B 670 (2009) 246)
bull The inhomogeneous equation of state (S Nojiri SD Odintsov Phys Rev D 72 (2005) 023003)
bull The continuity equation
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
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- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
The model dynamicsbull The dynamics of the Hubble parameter
bull Notation
bull Dynamics in terms of dimensionless parameters
bull with the initial condition
bull HX and a
X in principle arbitrary
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
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- Slide 37
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- Slide 39
- Slide 40
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- Slide 49
- Slide 50
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- Slide 76
- Slide 77
- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
α lt minus1 the relaxation mechanism forthe large cosmological constant
bull The α = minus3 case
bull Closed form solution
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
- Slide 21
- Slide 22
- Slide 23
- Slide 24
- Slide 25
- Slide 26
- Slide 27
- Slide 28
- Slide 29
- Slide 30
- Slide 31
- Slide 32
- Slide 33
- Slide 34
- Slide 35
- Slide 36
- Slide 37
- Slide 38
- Slide 39
- Slide 40
- Slide 41
- Slide 42
- Slide 43
- Slide 44
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- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
case
bull Late-time symptotic behavior
bull Ʌeff
is small because |Ʌ| is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
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- Slide 19
- Slide 20
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- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
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- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Dependence on model parameters
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 13
- Slide 14
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- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Dependence on model parameters
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 14
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- Slide 83
- Slide 84
- Slide 85
-
case
bull Asymptotic behavior
bull Late-time asymptotic behavior
bull Ʌeff
is small because Ʌ is large
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
- Slide 18
- Slide 19
- Slide 20
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- Slide 26
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- Slide 28
- Slide 29
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- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
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- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Dependence on model parameters
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Dependence on model parameters
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Dependence on model parameters
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 13
- Slide 14
- Slide 15
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- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Other parameter regimes
bull For α gt minus1 the behavior is differentbull The relaxation mechanism is not
automatic
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
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- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Fixed points approach to de Sitter regime
bull general dynamics
bull Fixed point rArr
bull Example rArr
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 81
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- Slide 83
- Slide 84
- Slide 85
-
General inhomogeneous EOS
bull dynamics of the scaled Hubble parameter
bull condition for the relaxation mechanism
bull for a small h at late-time
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 83
- Slide 84
- Slide 85
-
Variable cosmological term
bull Running CC
bull Extended running CC
bull Interaction with matter + put βn rarr 0
bull Dynamics of the Hubble parameter
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
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- Slide 14
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- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Variable cosmological term
bull Late-time asymptotic behavior
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
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- Slide 83
- Slide 84
- Slide 85
-
f(R) modified gravity
bull general dynamics
bull specific example
bull asymptotic de Sitter regime
bull n=1
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
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- Slide 78
- Slide 79
- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Important questions bull Abruptness of the transition
bull The onset of the transition
bull The connection to other eras of (accelerated) expansion
bull Addition of other components and other cosmological (RDMD) eras
bull Cosmological coincidence problem
bull Stability of the mechanism to perturbations
bull Precision tests and the comparisons with the observational datandash astrophysical scales (eg solar system tests)ndash cosmological scales (growth of inhomogeneities)
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
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- Slide 84
- Slide 85
-
Summary of the relaxation mechanism properties
bull The solution of the CC problem without fine-tuning for both signs of the CC
bull The universe with a large CC has a small positive positive effective CC
bull Ʌeff
is small because |Ʌ| is large
bull Ʌeff
~ 1|Ʌ|
bull candidate physical mechanisms modified gravity (nonlinear) viscosity quantum effects
bull Exchanging ldquounnaturalrdquo parameters for some new (not too complicated) dynamics
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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- Slide 84
- Slide 85
-
Relaxing a large cosmological constant - adding matter and radiation
bull F Bauer J Sola H Š arXiv09022215 bull Components
ndash variable cosmological term (containing a large constant term)
ndash dark matterndash baryons ndash radiation
bull Variable cosmological term and DM interact
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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-
The formalism
bull The variable cosmological termbull Constructing f from general coordinate
covariant terms
bull Interaction with the DM component
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
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- Slide 84
- Slide 85
-
frac12 Model
bull f=R
bull Radiation domination (controlled by 1-q)bull transition to de Sitter regime (controlled by
small H2)
bull abrupt transition removedbull RD phase introduced
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
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- Slide 84
- Slide 85
-
The model
bull Two terms dominated by different values of q and different powers of H
bull Sequence of a RD MD and de Sitter phases
bull Realistic cosmological model with a relaxed CC
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
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- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
The deceleration parameter
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
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- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Normalized energy densities
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
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- Slide 80
- Slide 81
- Slide 82
- Slide 83
- Slide 84
- Slide 85
-
Absolute energy densities
Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
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Effective DE EOS
Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
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Conclusions
bull The question of the mechanism of the acceleration of the universe still open
bull The cosmological constant problem(s) ndash many proposed approaches ndash decisive arguments still to come
bull The nexus of physics at many very different distanceenergy scales
bull Testing ground of the future theoretical observational and experimental efforts
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