Universe without Expansion
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Transcript of Universe without Expansion
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Universe without Expansion
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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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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 fieldEffective Planck mass depends on scalar field 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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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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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 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
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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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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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Radiation dominationRadiation domination
UniverseUniverseshrinks !shrinks !
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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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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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Model BModel B
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Radiation dominationRadiation dominationFlat 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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Weyl scalingWeyl scaling
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Kinetial Kinetial
scalar scalar σσ with withstandard normalizationstandard normalization
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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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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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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
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Growing neutrino Growing neutrino quintessencequintessence
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Observational bounds on Observational bounds on ΩΩhh
G.RobberG.Robbers , s , M.Doran ,M.Doran ,……
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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 ?
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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 Universe non-relativistic only in the late 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.
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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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Neutrinos in cosmologyNeutrinos in cosmology
only small fraction of energy only small fraction of energy densitydensity
only sub-leading role ?only sub-leading role ?
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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.
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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
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Neutrino cosmon Neutrino cosmon couplingcoupling
realized by dependence of neutrino massrealized by dependence of neutrino mass on value of cosmon fieldon value of cosmon field
β ≈ 1 β ≈ 1 : cosmon mediated attractive force : cosmon mediated attractive force between neutrinos has similar strength as between neutrinos has similar strength as gravitygravity
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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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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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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 !
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cosmon coupling to cosmon coupling to neutrinosneutrinos
basic ingredient :basic ingredient :
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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 to transition from early scaling solution to cosmological constant dominated cosmological constant dominated cosmologycosmology
L.Amendola,M.Baldi,…L.Amendola,M.Baldi,…
Fardon,Nelson,WeinerFardon,Nelson,Weiner
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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 )
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cosmon evolutioncosmon evolution
scaliscalingng
““stopped”stopped”
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neutrino lumpsneutrino lumps
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neutrino fluctuationsneutrino fluctuationsneutrino 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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Formation of neutrino Formation of neutrino lumpslumps
N- body simulation M.Baldi et N- body simulation M.Baldi et alal
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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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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,…
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importance of backreaction :importance of backreaction :cosmological average of cosmological average of
neutrino massneutrino massY.Ayaita , Y.Ayaita , E.Puchwein,…E.Puchwein,…
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importance of importance of backreaction :backreaction :
fraction in Dark Energyfraction in Dark Energy
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neutrino lumpsneutrino lumpsbehave 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,……
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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 variable electron masses are proportional to variable Planck massPlanck 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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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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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
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EnEndd
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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
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early scaling solution ( tracker early scaling solution ( tracker solution )solution )
neutrino mass unimportant in early cosmologyneutrino mass unimportant in early cosmology
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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
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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 !!
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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)
P.Viana, A.Liddle , Phys.Rev.D57,674(1998)P.Viana, A.Liddle , Phys.Rev.D57,674(1998)
E.Copeland,A.Liddle,D.Wands , Phys.Rev.D57,4686(1998)E.Copeland,A.Liddle,D.Wands , Phys.Rev.D57,4686(1998)
R.Caldwell,R.Dave,P.Steinhardt , Phys.Rev.Lett.80,1582(1998)R.Caldwell,R.Dave,P.Steinhardt , Phys.Rev.Lett.80,1582(1998)
P.Steinhardt,L.Wang,I.Zlatev , Phys.Rev.Lett.82,896(1999)P.Steinhardt,L.Wang,I.Zlatev , Phys.Rev.Lett.82,896(1999)