Universe without Expansion

The Universe is The Universe is shrinkingshrinking

The Universe is The Universe is shrinking …shrinking …

while Planck mass and while Planck mass and particle masses are particle masses are

increasingincreasing

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

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

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

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

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

QuintessenceQuintessence Dynamical dark Dynamical dark energy ,energy ,

generated by generated by scalarscalar fieldfield

(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

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

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

Model AModel A

μμ= 2 = 2 10 10-33 -33 eVeV

Scalar field Scalar field equationequation::

additional force from R additional force from R counteracts potential counteracts potential

gradient : increasing χ !gradient : increasing χ !

Modified Einstein Modified Einstein equationequation

New term with derivatives of scalar fieldNew term with derivatives of scalar field

Curvature scalar and Curvature scalar and Hubble parameterHubble parameter

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

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.

No big bang singularityNo big bang singularity

Radiation dominationRadiation domination

UniverseUniverseshrinks !shrinks !

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

cosmon coupling to cosmon coupling to mattermatter

qqχχ=-(ρ-3p)/χ=-(ρ-3p)/χ

Matter dominationMatter domination

Universe Universe shrinks !shrinks !

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

Model BModel B

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 )

Matter dominationMatter domination

Weyl scalingWeyl scaling

Kinetial Kinetial

scalar scalar σσ with withstandard normalizationstandard normalization

Inflation : Slow roll Inflation : Slow roll parametersparameters

End of End of inflationinflationat at εε = 1 = 1

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

Spectral index and Spectral index and tensor to scalar ratiotensor to scalar ratio

Model AModel A

Amplitude of density Amplitude of density fluctuationsfluctuations

Einstein frame , model BEinstein frame , model B

kk22

for large for large χχ : : no difference to model Ano difference to model A

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

conclusion 1conclusion 1

cosmon inflation :cosmon inflation : compatible with observationcompatible with observation simplesimple no big bang singularityno big bang singularity stability of solution singles out arrow stability of solution singles out arrow

of timeof time simple initial conditionssimple initial conditions

Growing neutrino Growing neutrino quintessencequintessence

Observational bounds on Observational bounds on ΩΩhh

G.RobberG.Robbers , s , M.Doran ,M.Doran ,……

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 ?

Why neutrinos may play Why neutrinos may play a rolea role

Mass scales :Mass scales :

Dark Energy density : Dark Energy density : ρρ ~ ( 2×10 ~ ( 2×10 -3-3 eV ) eV )- 4- 4..

Neutrino mass : eV or below.Neutrino mass : eV or below.

Cosmological trigger : Cosmological trigger : Neutrinos became Neutrinos became non-relativistic only in the late non-relativistic only in the late Universe .Universe .

Neutrino energy density Neutrino energy density not much not much smaller than Dark Energy density .smaller than Dark Energy density .

Neutrinos can have substantial Neutrinos can have substantial coupling coupling to Dark Energy.to Dark Energy.

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

Neutrinos in cosmologyNeutrinos in cosmology

only small fraction of energy only small fraction of energy densitydensity

only sub-leading role ?only sub-leading role ?

Neutrino cosmon Neutrino cosmon couplingcoupling

Strong bounds on atom-cosmon coupling from Strong bounds on atom-cosmon coupling from tests of equivalence principle or time variation tests of equivalence principle or time variation of couplings.of couplings.

No such bounds for neutrino-cosmon coupling.No such bounds for neutrino-cosmon coupling.

In particle physics : Mass generation In particle physics : Mass generation mechanism for neutrinos differs from charged mechanism for neutrinos differs from charged fermions. Seesaw mechanism involves heavy fermions. Seesaw mechanism involves heavy particles whose mass may depend on the value particles whose mass may depend on the value of the cosmon field. of the cosmon field.

neutrino massneutrino mass

seesaw seesaw andandcascadecascademechanismechanismm

omit generation omit generation structurestructure

triplet expectation value ~ doublet squaredtriplet expectation value ~ doublet squared

M.Magg, C.W. M.Magg, C.W. 1980 1980

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

growing neutrinos growing neutrinos change cosmon evolutionchange cosmon evolution

modification of conservation equation for neutrinosmodification of conservation equation for neutrinos

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,…

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 !

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

cosmological selectioncosmological selection

present value of dark energy density present value of dark energy density set by cosmological event :set by cosmological event :

neutrinos become non – relativistic neutrinos become non – relativistic

not given by ground state properties !not given by ground state properties !

cosmon coupling to cosmon coupling to neutrinosneutrinos

basic ingredient :basic ingredient :

Cosmon coupling to Cosmon coupling to neutrinosneutrinos

can be large !can be large !

interesting effects for cosmology if interesting effects for cosmology if neutrino mass is growingneutrino mass is growing

growing neutrinos can stop the growing neutrinos can stop the evolution of the cosmonevolution of the cosmon

transition from early scaling solution transition from early scaling solution to cosmological constant dominated to cosmological constant dominated cosmologycosmology

L.Amendola,M.Baldi,…L.Amendola,M.Baldi,…

Fardon,Nelson,WeinerFardon,Nelson,Weiner

stopped scalar fieldstopped scalar fieldmimicks amimicks a

cosmological constantcosmological constant( almost …)( almost …)

rough approximation for dark energy :rough approximation for dark energy : before redshift 5-6 : scaling ( dynamical ) before redshift 5-6 : scaling ( dynamical ) after redshift 5-6 : almost static after redshift 5-6 : almost static

( cosmological constant )( cosmological constant )

cosmon evolutioncosmon evolution

scaliscalingng

““stopped”stopped”

neutrino lumpsneutrino lumps

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 , …

Formation of neutrino Formation of neutrino lumpslumps

N- body simulation M.Baldi et N- body simulation M.Baldi et alal

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

Formation of neutrino Formation of neutrino lumpslumps

Y.Ayaita,M.Weber,…Y.Ayaita,M.Weber,…

backreactionbackreactioncosmon field inside lumps does cosmon field inside lumps does not follow not follow cosmological evolutioncosmological evolution

neutrino mass inside lumps neutrino mass inside lumps smaller than smaller than in environment in environment L.Schrempp, L.Schrempp, N.Nunes,…N.Nunes,…

importance of backreaction :importance of backreaction :cosmological average of cosmological average of

neutrino massneutrino mass

Y.Ayaita , Y.Ayaita , E.Puchwein,…E.Puchwein,…

importance of importance of backreaction :backreaction :

fraction in Dark Energyfraction in Dark Energy

neutrino lumpsneutrino lumps

behave as non-relativistic behave as non-relativistic fluid with fluid with effective coupling to effective coupling to cosmoncosmon Y.Ayaita,Y.Ayaita,

M.Weber,M.Weber,……

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

oscillating neutrino massoscillating neutrino mass

oscillating neutrino oscillating neutrino lumpslumps

small oscillations in dark small oscillations in dark energyenergy

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

Tests for growing Tests for growing neutrino quintessenceneutrino quintessence

Hubble parameterHubble parameteras compared to as compared to ΛΛCDMCDM

Hubble parameter ( z < Hubble parameter ( z < zzc c ))

only small only small differencedifferencefrom from ΛΛCDM !CDM !

bounds on average neutrino bounds on average neutrino massmass

Small induced enhancement Small induced enhancement of dark matter power of dark matter power

spectrum at large scalesspectrum at large scales

Enhanced bulk velocitiesEnhanced bulk velocities

Enhancement of Enhancement of gravitational potentialgravitational potential

Test of allowed parameter space by Test of allowed parameter space by ISW effectISW effect

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

ConclusionsConclusions

Cosmic event triggers qualitative Cosmic event triggers qualitative change in evolution of cosmonchange in evolution of cosmon

Cosmon stops changing after Cosmon stops changing after neutrinos become non-relativisticneutrinos become non-relativistic

Explains why nowExplains why now Cosmological selectionCosmological selection Model can be distinguished from Model can be distinguished from

cosmological constantcosmological constant

EnEndd

strong effective strong effective neutrino – cosmon neutrino – cosmon

coupling coupling for for φφ → → φφtt

typical present value : typical present value : ββ ≈≈ 50 50 cosmon mediated attraction between neutrinoscosmon mediated attraction between neutrinosis about 50is about 5022 stronger than gravitational attraction stronger than gravitational attraction

early scaling solution ( tracker early scaling solution ( tracker solution )solution )

neutrino mass unimportant in early cosmologyneutrino mass unimportant in early cosmology

dark energy fraction dark energy fraction determined by neutrino determined by neutrino

massmass

constant neutrino - cosmon coupling constant neutrino - cosmon coupling ββ

variable neutrino - cosmon couplingvariable neutrino - cosmon coupling

effective stop of cosmon effective stop of cosmon evolutionevolution

cosmon evolution almost stops cosmon evolution almost stops onceonce

neutrinos get non –relativisticneutrinos get non –relativistic ß gets largeß gets large

This alwaysThis alwayshappens happens for for φφ → → φφt t !!

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

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