Dilaton quantum gravity and cosmology
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Dilaton quantum Dilaton quantum gravity gravity
and cosmologyand cosmology
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Dilaton quantum gravityDilaton quantum gravity
Functional renormalization flow,Functional renormalization flow,
with truncation :with truncation :
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Functional renormalization Functional renormalization equationsequations
Percacci, Percacci, NarainNarain
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Fixed point for large Fixed point for large scalar fieldscalar field
This fixed point describes already This fixed point describes already realistic gravity !realistic gravity !Limit k → 0 can be taken !Limit k → 0 can be taken !
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Fixed point for large Fixed point for large scalar fieldscalar field
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Vicinity of fixed pointVicinity of fixed point
solution solution ::
Cosmology with dynamical dark energy Cosmology with dynamical dark energy !!Cosmological constant vanishes Cosmological constant vanishes asymptotically !asymptotically !
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open …open …
full scaling solutionfull scaling solution behavior for negative kinetic term behavior for negative kinetic term
close to close to
conformal valueconformal value
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a guess for a guess for dilaton quantum gravity dilaton quantum gravity
and its and its cosmological cosmological consequenceconsequence
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Crossover in quantum Crossover in quantum gravitygravity
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Approximate scale symmetry near fixed points
UV : approximate scale invariance of primordial fluctuation spectrum from inflation
IR : almost massless pseudo-Goldstone boson (cosmon) responsible for dynamical Dark Energy
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Variable GravityVariable Gravity
scale invariant for scale invariant for μμ= 0 and B = 0 and B const.const.quantum effects : flow equation quantum effects : flow equation for kinetialfor kinetial
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Variable GravityVariable Gravity
Scalar field coupled to gravityScalar field coupled to gravity Effective Planck mass depends on scalar fieldEffective Planck mass depends on scalar field Simple quadratic scalar potential involves Simple quadratic scalar potential involves
intrinsic mass intrinsic mass μμ Nucleon and electron mass proportional to Nucleon and electron mass proportional to
dynamical Planck massdynamical Planck mass Neutrino mass has different dependence on Neutrino mass has different dependence on
scalar fieldscalar field
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No tiny dimensionless No tiny dimensionless parametersparameters
( except gauge hierarchy )( except gauge hierarchy )
one mass scaleone mass scale
one time scale one time scale μμ-1-1 = 10 = 10 1010 yr yr
Planck mass does not appearPlanck mass does not appear Planck mass grows large dynamicallyPlanck mass grows large dynamically
μ = 2 μ = 2 10 10 -33 -33
eVeV
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Infrared fixed pointInfrared fixed point
μ→μ→ 0 0BB→→ 0 0
no intrinsic mass scaleno intrinsic mass scalescale symmetryscale symmetry
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Fixed points and limits Fixed points and limits for scalar fieldfor scalar field
Dimensionless functions as B Dimensionless functions as B
depend only on ratio depend only on ratio μμ//χχ . . IR: μ→0 , IR: μ→0 , χ→∞χ→∞ / y / y →∞→∞ UV: UV: μ→∞μ→∞ , , χ→χ→0 / y 0 / y →→0 0
Cosmology makes Cosmology makes
crossover betweencrossover between
fixed points byfixed points by
variation of variation of χχ . .
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Ultraviolet fixed pointUltraviolet fixed point
μ→μ→ ∞ ∞
kinetial divergeskinetial diverges
scale symmetry with anomalous scale symmetry with anomalous dimension dimension σσ
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Renormalized field at UV Renormalized field at UV fixed pointfixed point
no no massmassscalescaledeviation deviation fromfromfixed pointfixed pointvanishes forvanishes forμ→μ→ ∞ ∞
1 < 1 < σσ < < 22
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Asymptotic safetyAsymptotic safety
if UV fixed point exists :if UV fixed point exists :
quantum gravity is quantum gravity is
non-perturbatively non-perturbatively renormalizable !renormalizable !
S. Weinberg , M. S. Weinberg , M. ReuterReuter
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Quantum scale symmetryQuantum scale symmetry
quantum fluctuations violate scale quantum fluctuations violate scale symmetrysymmetry
running dimensionless couplingsrunning dimensionless couplings at fixed points , scale symmetry is at fixed points , scale symmetry is
exact !exact !
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Crossover between two Crossover between two fixed pointsfixed points
m : scale of crossoverm : scale of crossovercan be exponentially larger than intrinsic scale can be exponentially larger than intrinsic scale μμ
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Origin of massOrigin of mass UV fixed point : UV fixed point : scale symmetry unbrokenscale symmetry unbroken
all particles are masslessall particles are massless
IR fixed point : IR fixed point : scale symmetry spontaneously scale symmetry spontaneously brokenbroken, ,
massive particles , massless dilatonmassive particles , massless dilaton
crossover : crossover : explicit mass scale explicit mass scale μμ or m important or m important
SM fixed point : SM fixed point : approximate scale symmetryapproximate scale symmetry spontaneously brokenspontaneously broken, , massive particles , almost massive particles , almost massless cosmon, tiny cosmon potentialmassless cosmon, tiny cosmon potential
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Cosmological solution :Cosmological solution :crossover from UV to IR crossover from UV to IR
fixed pointfixed point Dimensionless functions as B Dimensionless functions as B
depend only on ratio depend only on ratio μμ//χχ . . IR: μ→0 , IR: μ→0 , χ→∞χ→∞ UV: UV: μ→∞μ→∞ , , χ→χ→00
Cosmology makes Cosmology makes
crossover betweencrossover between
fixed points byfixed points by
variation of variation of χχ . .
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SimplicitySimplicity
simple description of simple description of allall cosmological cosmological epochsepochs
natural incorporation of Dark Energy :natural incorporation of Dark Energy : inflationinflation Early Dark EnergyEarly Dark Energy present Dark Energy dominated epochpresent Dark Energy dominated epoch
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Model is compatible with present observations
Together with variation of neutrino mass over electron mass during second stage of crossover :
model is compatible with all present observations
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ExpansionExpansion
Inflation : Universe expandsInflation : Universe expands Radiation : Universe shrinksRadiation : Universe shrinks Matter : Universe shrinksMatter : Universe shrinks Dark Energy : Universe expandsDark Energy : Universe expands
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Big bang or freeze Big bang or freeze ??
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NATURENATURE | NEWS | NEWS
Cosmologist claims Universe may not be Cosmologist claims Universe may not be expandingexpandingParticles' changing masses could Particles' changing masses could explain why distant galaxies appear to explain why distant galaxies appear to be rushing away.be rushing away.
Jon CartwrightJon Cartwright 16 July 201316 July 2013
German physicist German physicist stops Universestops Universe25.07.201325.07.2013
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SonntagszeitungSonntagszeitungZürichZürichLaukenmannLaukenmann
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The Universe is The Universe is shrinkingshrinking
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The Universe is The Universe is shrinking …shrinking …
while Planck mass and while Planck mass and particle masses are particle masses are
increasingincreasing
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RedshiftRedshift
instead of redshift due to expansion :instead of redshift due to expansion :
smaller frequencies have been smaller frequencies have been emitted in the past, because electron emitted in the past, because electron mass was smaller !mass was smaller !
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What is increasing ?What is increasing ?
Ratio of distance between galaxies Ratio of distance between galaxies over size of atoms !over size of atoms !
atom size constant : expanding geometryatom size constant : expanding geometry
alternative : shrinking size of atomsalternative : shrinking size of atoms
general idea not new : Hoyle, general idea not new : Hoyle, Narlikar,…Narlikar,…
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Different pictures of Different pictures of cosmologycosmology
same physical content can be same physical content can be described by different picturesdescribed by different pictures
related by field – related by field – redefinitionsredefinitions , , e.g. Weyl scaling , e.g. Weyl scaling , conformal scaling of metricconformal scaling of metric
which picture is usefull ?which picture is usefull ?
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Cosmological scalar field Cosmological scalar field ( cosmon )( cosmon )
scalar field is crucial ingredient scalar field is crucial ingredient particle masses proportional to scalar particle masses proportional to scalar
field – similar to Higgs fieldfield – similar to Higgs field particle masses increase because particle masses increase because
value of scalar field increasesvalue of scalar field increases scalar field plays important role in scalar field plays important role in
cosmologycosmology cosmon : pseudo Goldstone boson of cosmon : pseudo Goldstone boson of
spontaneously broken scale symmetryspontaneously broken scale symmetry
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Cosmon inflationCosmon inflation
Unified picture of inflation and Unified picture of inflation and dynamical dark energydynamical dark energy
Cosmon and inflaton are the Cosmon and inflaton are the same scalar fieldsame scalar field
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QuintessenceQuintessence
Dynamical dark energy ,Dynamical dark energy ,
generated by scalargenerated by scalar field field (cosmon )(cosmon )
C.Wetterich,Nucl.Phys.B302(1988)668, C.Wetterich,Nucl.Phys.B302(1988)668, 24.9.8724.9.87P.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)L17, P.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)L17, 20.10.8720.10.87
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Prediction :Prediction :
homogeneous dark energy homogeneous dark energyinfluences recent cosmologyinfluences recent cosmology
- of same order as dark - of same order as dark matter -matter -
Original models do not fit the present observationsOriginal models do not fit the present observations … …. modifications . modifications ( different growth of neutrino mass )( different growth of neutrino mass )
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Hot plasma ?Hot plasma ?
Temperature in radiation dominated Temperature in radiation dominated Universe : T ~ Universe : T ~ χχ ½½ smallersmaller than today than today
Ratio temperature / particle mass : Ratio temperature / particle mass : T /m T /mpp ~ ~ χχ --½½ largerlarger than today than today
T/mT/mpp counts ! This ratio decreases with counts ! This ratio decreases with time.time.
Nucleosynthesis , CMB emission as in Nucleosynthesis , CMB emission as in standard cosmology ! standard cosmology !
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Infinite past : slow Infinite past : slow inflationinflation
σσ = 2 : field equations = 2 : field equations
solutionsolution
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Slow UniverseSlow Universe
Expansion or shrinking always slow ,Expansion or shrinking always slow , characteristic time scale of the order of the characteristic time scale of the order of the age of theage of the Universe : Universe : ttch ch ~~ μμ-1 -1 ~ ~ 10 billion years10 billion years ! !Hubble parameter of the order of Hubble parameter of the order of presentpresent Hubble Hubble parameter for all times , including inflation parameter for all times , including inflation and big bang !and big bang !Slow increase of particle masses ! Slow increase of particle masses !
μμ= 2 = 2 10 10-33 -33 eVeV
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Spectrum of primordial density Spectrum of primordial density fluctuationsfluctuations
tensortensoramplituamplitudede
spectspectralralindexindex
rather rather large !large !
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Anomalous dimension Anomalous dimension determines spectrum of determines spectrum of primordial fluctuationsprimordial fluctuations
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Amplitude of density Amplitude of density fluctuationsfluctuations
small because of logarithmic small because of logarithmic running running near UV fixed point !near UV fixed point !
N : number of e – foldings at horizon N : number of e – foldings at horizon crossing crossing
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First step of crossover First step of crossover ends inflationends inflation
induced by crossover in Binduced by crossover in B
after crossover B changes only very after crossover B changes only very slowlyslowly
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Scaling solutions Scaling solutions near SM fixed pointnear SM fixed point
( approximation for constant B ( approximation for constant B ))
Different scaling solutions Different scaling solutions forforradiation domination and radiation domination and matter dominationmatter domination
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conclusionsconclusions
crossover in quantum gravity is reflected in crossover in quantum gravity is reflected in crossover in cosmologycrossover in cosmology
quantum gravity becomes testable by quantum gravity becomes testable by cosmologycosmology
quantum gravity plays a role not only for quantum gravity plays a role not only for primordial cosmologyprimordial cosmology
crossover scenario explains different crossover scenario explains different cosmological epochscosmological epochs
simple model is compatible with present simple model is compatible with present observationsobservations
no more parameters than no more parameters than ΛΛCDM CDM : : tests possibletests possible
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endend
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Einstein frameEinstein frame
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Einstein frameEinstein frame
Weyl scaling maps variable gravity Weyl scaling maps variable gravity model to Universe with fixed masses model to Universe with fixed masses and standard expansion history.and standard expansion history.
Standard gravity coupled to scalar Standard gravity coupled to scalar field.field.
Only neutrino masses are growing.Only neutrino masses are growing.