Universe without Expansion
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Transcript of Universe without Expansion
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Universe without Expansion
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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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SonntagszeitungSonntagszeitungZuerichZuerichLaukenmannLaukenmann
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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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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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Two models ofTwo models of “ Variable Gravity “ Variable Gravity
Universe “Universe “ Scalar field coupled to gravityScalar field coupled to gravity Effective Planck mass depends on scalar Effective Planck mass depends on scalar
fieldfield Simple scalar potential :Simple scalar potential :
quadratic ( model A )quadratic ( model A )
cosmological constant ( model B )cosmological constant ( model B ) Nucleon and electron mass proportional to Nucleon and electron mass proportional to
Planck massPlanck mass Neutrino mass has different dependence on Neutrino mass has different dependence on
scalar fieldscalar field
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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 :inflationinflationEarly Dark EnergyEarly Dark Energypresent Dark Energy dominated epochpresent Dark Energy dominated epoch
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Model AModel A
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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Model BModel B
Inflation : Universe expandsInflation : Universe expands Radiation : Static Minkowski Radiation : Static Minkowski
spacespace Matter : Universe expandsMatter : Universe expands Dark Energy : Universe expandsDark Energy : Universe expands
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Compatibility with Compatibility with observationsobservations
Both models lead to same predictions for Both models lead to same predictions for radiation, matter , and Dark Energy radiation, matter , and Dark Energy domination, domination, despite the very different despite the very different expansion historyexpansion history
Different inflation models:Different inflation models:
A: n=0.97, r=0.13 B: n=0.95, r=0.04A: n=0.97, r=0.13 B: n=0.95, r=0.04 Almost same prediction for radiation, matter, Almost same prediction for radiation, matter,
and Dark Energy domination as and Dark Energy domination as ΛΛCDMCDM Presence of small fraction of Early Dark Presence of small fraction of Early Dark
EnergyEnergy Large neutrino lumpsLarge neutrino lumps
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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.
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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 fieldsame 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
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Merits of variable gravity Merits of variable gravity modelsmodels
Economical settingEconomical setting No big bang singularityNo big bang singularity Arrow of timeArrow of time Simple initial conditions for inflationSimple initial conditions for inflation
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Model AModel A
μμ= 2 = 2 10 10-33 -33 eVeV
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Scalar field Scalar field equationequation::
additional force from R additional force from R counteracts potential counteracts potential
gradient : increasing χ !gradient : increasing χ !
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Incoherent contribution Incoherent contribution to scalar field equationto scalar field equation
if particle massif particle massproportional to proportional to χ :χ :
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Modified Einstein Modified Einstein equationequation
New term with derivatives of scalar fieldNew term with derivatives of scalar field
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Curvature scalar and Curvature scalar and Hubble parameterHubble parameter
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Scaling solutionsScaling solutions( for constant K )( for constant K )
Four different scaling Four different scaling solutions forsolutions forinflation, radiation inflation, radiation domination, domination, matter domination andmatter domination andDark Energy dominationDark Energy domination
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Scalar dominated epoch, Scalar dominated epoch, inflationinflation
Universe expands for K > -4, shrinks for K < -4.Universe expands for K > -4, shrinks for K < -4.
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No big bang singularityNo big bang singularity
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Scaling solution is Scaling solution is attractiveattractive
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Scaling solution ends Scaling solution ends when K gets closer to -6when K gets closer to -6
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Radiation dominationRadiation domination
UniverseUniverseshrinks !shrinks !
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Early Dark EnergyEarly Dark Energy
Energy density in radiation Energy density in radiation increases , increases , proportional to cosmon proportional to cosmon potentialpotential
fraction in early dark fraction in early dark energyenergy
requires large requires large α >10α >10
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scaling of particle scaling of particle massesmasses
mass of electron or nucleon is proportionalmass of electron or nucleon is proportionalto variable Planck mass to variable Planck mass χχ ! !
effective potential for Higgs doublet heffective potential for Higgs doublet h
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cosmon coupling to cosmon coupling to mattermatter
qqχχ=-(ρ-3p)/χ=-(ρ-3p)/χ
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Matter dominationMatter domination
Universe Universe shrinks !shrinks !
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Neutrino massNeutrino mass
seesaw seesaw andandcascadecascademechanismechanismm
omit generation omit generation structurestructure
triplet expectation value ~ doublet squaredtriplet expectation value ~ doublet squared
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Neutrino massNeutrino mass
assume that singlet scale has not yet reached assume that singlet scale has not yet reached scaling limit ~ scaling limit ~ χχ
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Dark Energy dominationDark Energy domination
neutrino masses scaleneutrino masses scaledifferently from electron massdifferently from electron mass
new scaling solution. not yet reached.new scaling solution. not yet reached.at present : transition periodat present : transition period
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Why now problemWhy now problem
Why does fraction in Dark Why does fraction in Dark Energy increase Energy increase in present cosmological epoch ,in present cosmological epoch ,and not much earlier or much and not much earlier or much later ?later ? neutrinos becomeneutrinos become
non-relativisticnon-relativisticat z = 5at z = 5
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Model BModel B
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Radiation dominationRadiation domination
Flat static Minkowski space ! H=0 ! Flat static Minkowski space ! H=0 !
constant energyconstant energydensitydensity
exact regular solution ! (constant K )exact regular solution ! (constant K )
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Matter dominationMatter domination
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ObservationsObservations
simplest description in Einstein simplest description in Einstein frameframe
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Weyl scalingWeyl scaling
(A)(A)
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Kinetial Kinetial
scalar scalar σσ with withstandard normalizationstandard normalization
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Cosmon inflationCosmon inflation
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Inflation : Slow roll Inflation : Slow roll parametersparameters
End of End of inflationinflationat at εε = 1 = 1
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Number of e-foldings Number of e-foldings before end of inflationbefore end of inflation
εε, η, N can all be , η, N can all be computed computed from kinetial alonefrom kinetial alone
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Spectral index and Spectral index and tensor to scalar ratiotensor to scalar ratio
Model AModel A
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Amplitude of density Amplitude of density fluctuationsfluctuations
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Properties of density Properties of density fluctuations , model Afluctuations , model A
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Einstein frame , model BEinstein frame , model B
kk22
for large for large χχ : : no difference to model Ano difference to model A
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inflation model Binflation model B
approximate relation between r and napproximate relation between r and n
n=0.95 , r=0.035n=0.95 , r=0.035
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Properties of density Properties of density fluctuations, model Bfluctuations, model B
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conclusion 1conclusion 1
cosmon inflation :cosmon inflation : compatible with observationcompatible with observation simplesimpleno big bang singularityno big bang singularitystability of solution singles out arrow stability of solution singles out arrow of timeof timesimple initial conditionssimple initial conditions
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Growing neutrino Growing neutrino quintessencequintessence
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connection between dark connection between dark energy energy
and neutrino propertiesand neutrino properties
present present equationequationof state given of state given bybyneutrino mass neutrino mass !!
present dark energy density given by neutrino masspresent dark energy density given by neutrino mass
= 1.27= 1.27
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Neutrino cosmon Neutrino cosmon couplingcoupling
realized by dependence of neutrino realized by dependence of neutrino massmass on value of cosmon field on value of cosmon field
β ≈ 1 β ≈ 1 : cosmon mediated attractive force : cosmon mediated attractive force between neutrinos has similar strength between neutrinos has similar strength as gravityas gravity
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growing neutrinos growing neutrinos change cosmon evolutionchange cosmon evolution
modification of conservation equation for neutrinosmodification of conservation equation for neutrinos
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growing neutrino mass growing neutrino mass triggers transition to triggers transition to
almost static dark energyalmost static dark energy
growinggrowingneutrinoneutrinomassmass
L.Amendola, M.Baldi,…L.Amendola, M.Baldi,…
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effective cosmological effective cosmological triggertrigger
for stop of cosmon for stop of cosmon evolution :evolution :
neutrinos get non-neutrinos get non-relativisticrelativistic
this has happened recently !this has happened recently ! sets scales for dark energy !sets scales for dark energy !
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cosmon evolutioncosmon evolution
scaliscalingng
““stopped”stopped”
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neutrino lumpsneutrino lumps
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neutrino fluctuationsneutrino fluctuations
neutrino structures become nonlinear neutrino structures become nonlinear at z~1 for supercluster scalesat z~1 for supercluster scales
stable neutrino-cosmon lumps exist stable neutrino-cosmon lumps exist N.Brouzakis , N.Tetradis ,… ; O.Bertolami ; Y.Ayaita , N.Brouzakis , N.Tetradis ,… ; O.Bertolami ; Y.Ayaita , M.Weber,…M.Weber,…
D.Mota , G.Robbers , V.Pettorino , …D.Mota , G.Robbers , V.Pettorino , …
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N-body code with fully N-body code with fully relativistic neutrinos and relativistic neutrinos and
backreactionbackreaction
Y.Ayaita,M.WebY.Ayaita,M.Weber,…er,…
one has to resolve local value of one has to resolve local value of cosmon fieldcosmon fieldand then form cosmological and then form cosmological average;average;similar for neutrino density, dark similar for neutrino density, dark matter and matter and gravitational fieldgravitational field
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Formation of neutrino Formation of neutrino lumpslumps
Y.Ayaita,M.Weber,…Y.Ayaita,M.Weber,…
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φφ - dependent neutrino – - dependent neutrino – cosmon couplingcosmon coupling
neutrino lumps form and are disrupted by neutrino lumps form and are disrupted by oscillations in neutrino massoscillations in neutrino masssmaller backreaction smaller backreaction
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oscillating neutrino massoscillating neutrino mass
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oscillating neutrino oscillating neutrino lumpslumps
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small oscillations in dark small oscillations in dark energyenergy
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conclusionsconclusions
Variable gravity cosmologies can give a Variable gravity cosmologies can give a simple and realistic description of Universesimple and realistic description of Universe
Compatible with tests of equivalence Compatible with tests of equivalence principle and bounds on variation of principle and bounds on variation of fundamental couplings if nucleon and fundamental couplings if nucleon and electron masses are proportional to electron masses are proportional to variable Planck massvariable Planck mass
Different cosmon dependence of neutrino Different cosmon dependence of neutrino mass can explain why Universe makes a mass can explain why Universe makes a transition to Dark Energy domination transition to Dark Energy domination nownow
characteristic signal : neutrino lumpscharacteristic signal : neutrino lumps
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EnEndd
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Tests for growing Tests for growing neutrino quintessenceneutrino quintessence
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Hubble parameterHubble parameteras compared to as compared to ΛΛCDMCDM
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Hubble parameter ( z < Hubble parameter ( z < zzc c ))
only small only small differencedifferencefrom from ΛΛCDM !CDM !
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bounds on average neutrino bounds on average neutrino massmass
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Small induced enhancement Small induced enhancement of dark matter power of dark matter power
spectrum at large scalesspectrum at large scales
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Enhanced bulk velocitiesEnhanced bulk velocities
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Enhancement of Enhancement of gravitational potentialgravitational potential
Test of allowed parameter space by Test of allowed parameter space by ISW effectISW effect
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Can time evolution of Can time evolution of neutrino mass be neutrino mass be
observed ?observed ?Experimental determination of neutrino mass Experimental determination of neutrino mass
may turn out higher than cosmological upper may turn out higher than cosmological upper bound in model with constant neutrino massbound in model with constant neutrino mass
( KATRIN, neutrino-less double beta decay )( KATRIN, neutrino-less double beta decay )
GERDAGERDA
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A few early references on quintessenceA few early references on quintessence
C.Wetterich , Nucl.Phys.B302,668(1988) , received 24.9.1987C.Wetterich , Nucl.Phys.B302,668(1988) , received 24.9.1987
P.J.E.Peebles,B.Ratra , Astrophys.J.Lett.325,L17(1988) , received 20.10.1987P.J.E.Peebles,B.Ratra , Astrophys.J.Lett.325,L17(1988) , received 20.10.1987
B.Ratra,P.J.E.Peebles , Phys.Rev.D37,3406(1988) , received 16.2.1988B.Ratra,P.J.E.Peebles , Phys.Rev.D37,3406(1988) , received 16.2.1988
J.Frieman,C.T.Hill,A.Stebbins,I.Waga , Phys.Rev.Lett.75,2077(1995)J.Frieman,C.T.Hill,A.Stebbins,I.Waga , Phys.Rev.Lett.75,2077(1995)
P.Ferreira, M.Joyce , Phys.Rev.Lett.79,4740(1997)P.Ferreira, M.Joyce , Phys.Rev.Lett.79,4740(1997)
C.Wetterich , Astron.Astrophys.301,321(1995)C.Wetterich , Astron.Astrophys.301,321(1995)
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