QuintessenceQuintessence -- aa fifthfifth forceforce fromfrom variationvariation ofof thethe fundamentalfundamental scalescale ΩΩmm ++ XX == 11

? ΩΩmm :: 25%25%

ΩΩhh :: 75%75% DarkDark EnergyEnergy QuintessenceQuintessence

C.WetterichC.Wetterich

A.Hebecker,M.Doran,M.Lilley,J.SchwindtA.Hebecker,M.Doran,M.Lilley,J.Schwindt,, C.MC.Müüller,G.Schller,G.Schääfer,E.Thommesfer,E.Thommes,, R.Caldwell,M.Bartelmann,K.KarwanR.Caldwell,M.Bartelmann,K.Karwan DarkDark EnergyEnergy dominatesdominates thethe UniverseUniverse

EnergyEnergy -- densitydensity inin thethe UniverseUniverse == MatterMatter ++ DarkDark EnergyEnergy

2525 %% ++ 7575 %% MatterMatter :: EverythingEverything thatthat clumpsclumps

Abell 2255 Cluster ~300 Mpc ΩΩmm== 0.250.25

gravitational lens , HST ΩΩtottot=1=1 DarkDark EnergyEnergy

ΩΩmm ++ XX == 11

ΩΩmm :: 25%25%

ΩΩhh :: 75%75% DarkDark EnergyEnergy h : homogenous , often ΩΛ instead of Ωh SpaceSpace betweenbetween clumpsclumps isis notnot emptyempty ::

DarkDark EnergyEnergy !! DarkDark EnergyEnergy densitydensity isis thethe samesame atat everyevery pointpoint ofof spacespace

““ homogeneoushomogeneous ““

ΩΩhh PredictionsPredictions forfor darkdark energyenergy cosmologiescosmologies

The expansion of the Universe accelerates today ! What is Dark Energy ?

Cosmological Constant or Quintessence ? CosmologicalCosmological ConstantConstant -- EinsteinEinstein --

„ ConstantConstant λλ compatiblecompatible withwith allall symmetriessymmetries „ NoNo timetime variationvariation inin contributioncontribution toto energyenergy densitydensity

„ WhyWhy soso smallsmall ?? λλ/M/M4 == 1010-120

„ WhyWhy importantimportant justjust todaytoday ?? Cosm. Const. | Quintessence static | dynamical QuintessenceQuintessence andand solutionsolution ofof cosmologicalcosmological constantconstant problemproblem shouldshould bebe relatedrelated !! CosmologicalCosmological massmass scalesscales

„ Energy density „ Reduced Planck mass M=2.44×1018GeV ρ ~ ( 2.4×10 -3 eV )- 4 „ Newton’s constant

GN=(8πM²)

Only ratios of mass scales are observable !

4 homogeneous dark energy: ρh/M = 6.5 10¯¹²¹

4 matter: ρm/M = 3.5 10¯¹²¹ TimeTime evolutionevolution

t¯² matter dominated universe „ ρρ /M/M4 ~~ aa¯¯³³ ~~ m t¯3/2 radiation dominated universe

4 44 -2 „ ρρr/M/M ~~ aa¯¯ ~~ tt radiationradiation dominateddominated universeuniverse

HugeHuge ageage smallsmall ratioratio SameSame explanationexplanation forfor smallsmall darkdark energyenergy ?? TimeTime dependentdependent DarkDark EnergyEnergy :: QuintessenceQuintessence

„ What changes in time ?

„ OnlyOnly dimensionlessdimensionless ratiosratios ofof massmass scalesscales areare observableobservable !!

„ V : potential energy of scalar field or cosmological constant „ V/M4 is observable

„ ImagineImagine thethe PlanckPlanck massmass MM increasesincreases …… QuintessenceQuintessence fromfrom timetime evolutionevolution ofof fundamentalfundamental massmass scalescale FundamentalFundamental massmass scalescale

„ UnificationUnification fixesfixes parametersparameters withwith dimensionsdimensions

„ SpecialSpecial relativityrelativity :: cc „ QuantumQuantum theorytheory :: hh „ UnificationUnification withwith gravitygravity :: fundamentalfundamental massmass scalescale (( PlanckPlanck massmass ,, stringstring tensiontension ,, ……)) FundamentalFundamental massmass scalescale

„„ FixedFixed parameterparameter oror dynamicaldynamical scalescale ?? „„ DynamicalDynamical scalescale FieldField „„ DynamicalDynamical scalescale comparedcompared toto whatwhat ?? momentummomentum versusversus massmass (( oror otherother parameterparameter withwith dimensiondimension )) CosmonCosmon andand fundamentalfundamental massmass scalescale

„ AssumeAssume allall massmass parametersparameters areare proportionalproportional toto scalarscalar fieldfield χχ ((GUTsGUTs,, superstrings,superstrings,……))

„ MMp~~ χχ ,, mmproton~~ χχ ,, ΛΛQCD~~ χχ ,, MMW~~ χχ ,,……

„ χχ maymay evolveevolve withwith timetime :: cosmoncosmon

„ mmn/M/M :: (( almostalmost )) constantconstant -- observationobservation !!

OnlyOnly ratiosratios ofof massmass scalesscales areare observableobservable ExampleExample ::

FieldField χχ denotesdenotes scalescale ofof transitiontransition fromfrom higherhigher dimensionaldimensional physicsphysics toto effectiveeffective fourfour dimensionaldimensional descriptiondescription inin theorytheory withoutwithout fundamentalfundamental massmass parameterparameter

(except(except forfor runningrunning ofof dimensionlessdimensionless couplingscouplings……)) DilatationDilatation symmetrysymmetry

„ LagrangeLagrange density:density:

„ DilatationDilatation symmetrysymmetry forfor

„ ConformalConformal symmetrysymmetry forfor δδ=0=0 DilatationDilatation anomalyanomaly

„ QuantumQuantum fluctuationsfluctuations responsibleresponsible forfor dilatationdilatation anomalyanomaly „ RunningRunning couplings:couplings: hypothesishypothesis

„ RenormalizationRenormalization scalescale µµ:: (( momentummomentum scalescale )) „ λλ~(~(χχ//µµ)) –A „ EE >> 00 :: crossovercrossover QuintessenceQuintessence DilatationDilatation anomalyanomaly andand quantumquantum fluctuationsfluctuations

„ ComputationComputation ofof runningrunning couplingscouplings (( betabeta functionsfunctions )) needsneeds unifiedunified theorytheory !! „ DominantDominant contributioncontribution fromfrom modesmodes withwith momentamomenta ~~χχ !! „ NoNo prejudiceprejudice onon ““naturalnatural valuevalue ““ ofof anomalousanomalous dimensiondimension shouldshould bebe inferredinferred fromfrom tinytiny contributionscontributions atat QCDQCD-- momentummomentum scalescale !! CosmologyCosmology

CosmologyCosmology :: χχ increasesincreases withwith timetime !! (( duedue toto couplingcoupling ofof χχ toto curvaturecurvature scalarscalar )) forfor largelarge χχ thethe ratioratio V/MV/M4 decreasesdecreases toto zerozero

EffectiveEffective cosmologicalcosmological constantconstant vanishesvanishes asymptoticallyasymptotically forfor largelarge tt !! AsymptoticallyAsymptotically vanishingvanishing effectiveeffective ““cosmologicalcosmological constantconstant””

„ EffectiveEffective cosmologicalcosmological constantconstant ~~ V/MV/M4

„ λλ ~~ ((χχ//µµ)) –A

„ VV ~~ ((χχ//µµ)) –A χχ4

„ MM == χχ

V/MV/M4 ~(~(χχ//µµ)) –A WeylWeyl scalingscaling

2 WeylWeyl scalingscaling :: ggµν→→ (M/(M/χχ)) ggµν , φφ/M/M == lnln ((χχ 4/V(/V(χχ))))

ExponentialExponential potentialpotential :: VV == MM4 exp(exp(--φφ/M)/M) NoNo additionaladditional constantconstant !! Without dilatation – anomaly : V= const. Massless Goldstone boson = dilaton

Dilatation – anomaly : V (φ ) Scalar with tiny time dependent mass : cosmon CrossoverCrossover QuintessenceQuintessence

( like QCD gauge coupling) critical χ where δ grows large critical φ where k grows large k²(φ )=δ(χ)/4

k²(φ )= “1/(2E(φc – φ)/M)”

ifif ϕϕ c ≈≈ 276/M276/M (( tuningtuning !! )) ::

thisthis willwill bebe responsibleresponsible forfor relativerelative increaseincrease ofof darkdark energyenergy inin presentpresent cosmologicalcosmological epochepoch RealisticRealistic cosmologycosmology

HypothesisHypothesis onon runningrunning couplingscouplings yieldsyields realisticrealistic cosmologycosmology forfor suitablesuitable valuesvalues ofof AA ,, EE ,, φφc QuintessenceQuintessence cosmologycosmology QuintessenceQuintessence DynamicalDynamical darkdark energyenergy ,, generatedgenerated byby scalarscalar fieldfield

((cosmoncosmon))

C.Wetterich,Nucl.Phys.B302(1988)668, 24.9.8724.9.87 P.J.E.Peebles,B.Ratra,ApJ.Lett.325(1988)L17, 20.10.87 PredictionPrediction ::

homogeneoushomogeneous darkdark energyenergy influencesinfluences recentrecent cosmologycosmology

-- ofof samesame orderorder asas darkdark mattermatter --

OriginalOriginal modelsmodels dodo notnot fitfit thethe presentpresent observationsobservations …….. ModificationsModifications (( i.e.i.e. EE >> 00 )) QuintessenceQuintessence

CosmonCosmon –– FieldField φφ((x,y,z,tx,y,z,t))

HomogeneousHomogeneous undund isotropicisotropic UniverseUniverse :: φφ((x,y,z,tx,y,z,t)=)=φφ(t)(t)

PotentialPotential undund kinetickinetic energyenergy ofof thethe cosmoncosmon --fieldfield contributecontribute toto aa dynamicaldynamical energyenergy densitydensity ofof thethe UniverseUniverse !! ““FundamentalFundamental”” InteractionsInteractions

Strong, electromagnetic, weak interactions On astronomical length scales:

graviton

+

cosmon gravitation cosmodynamics DynamicsDynamics ofof quintessencequintessence

„ CosmonCosmon ϕϕ :: scalarscalar singletsinglet fieldfield

„ LagrangeLagrange densitydensity LL == VV ++ ½½ k(k(φφ)) ∂∂ϕϕ ∂∂ϕϕ (units: reduced Planck mass M=1)

„ PotentialPotential :: V=exp[V=exp[--ϕ]ϕ]

„ ““NaturalNatural initialinitial valuevalue”” inin PlanckPlanck eraera ϕ=0ϕ=0

„ today:today: ϕϕ=276=276 QuintessenceQuintessence modelsmodels

„ Kinetic function k(φ) : parameterizes the details of the model - “kinetial”

„ k(φ) = k=const. Exponential Q.

„ k(φ ) = exp ((φ – φ1)/α) Inverse power law Q. „ k²(φ )= “1/(2E(φc – φ))” Crossover Q.

„ possible naturalness criterion:

k(φ=0)/ k(φtoday) : not tiny or huge !

- else: explanation needed - CosmonCosmon

„„ ScalarScalar fieldfield changeschanges itsits valuevalue eveneven inin thethe presentpresent cosmologicalcosmological epochepoch „„ PotentialPotential undund kinetickinetic energyenergy ofof cosmoncosmon contributecontribute toto thethe energyenergy densitydensity ofof thethe UniverseUniverse „„ TimeTime -- variablevariable darkdark energyenergy ::

ρρhh(t(t)) decreasesdecreases withwith timetime !! CosmonCosmon

„„ TinyTiny massmass

„„ mmcc ~~ HH

„„ NewNew longlong -- rangerange interactioninteraction cosmoncosmon massmass changeschanges withwith timetime !!

forfor standardstandard kinetickinetic termterm 2 „ mmc == VV””

forfor standardstandard exponentialexponential potentialpotential ,, kk ≈≈ const.const. 2 2 2 2 „ mmc == VV””// kk == V/(V/( kk MM )) 2 2 == 33 ΩΩh (1(1 -- wwh )) HH /(/( 22 kk )) CosmologicalCosmological equationsequations CosmicCosmic AttractorsAttractors

Solutions independent of initial conditions typically V~t -2

φ ~ ln ( t )

Ωh ~ const. early cosmology details depend on V(φ) or kinetic term QuintessenceQuintessence becomesbecomes importantimportant ““todaytoday”” EquationEquation ofof statestate

p=Tp=T--VV pressurepressure kinetic energy ρρ=T+V=T+V energyenergy densitydensity

EquationEquation ofof statestate

DependsDepends onon specificspecific evolutionevolution ofof thethe scalarscalar fieldfield NegativeNegative pressurepressure

„ ww << 00 ΩΩh increasesincreases (with decreasing z ) late universe with small radiation component :

„ ww << --1/31/3 expansionexpansion ofof thethe UniverseUniverse isis acceleratingaccelerating

„ ww == --11 cosmologicalcosmological constantconstant QuintessenceQuintessence becomesbecomes importantimportant ““todaytoday””

NoNo reasonreason whywhy ww shouldshould bebe constantconstant inin timetime !! HowHow cancan quintessencequintessence bebe distinguisheddistinguished fromfrom aa cosmologicalcosmological constantconstant ?? TimeTime dependencedependence ofof darkdark energyenergy

-3 cosmological constant : Ωh ~ t² ~ (1+z) M.Doran,… smallsmall earlyearly andand largelarge presentpresent darkdark energyenergy fractionfraction inin darkdark energyenergy hashas substantiallysubstantially increasedincreased sincesince endend ofof structurestructure formationformation expansionexpansion ofof universeuniverse acceleratesaccelerates inin presentpresent epochepoch EarlyEarly darkdark energyenergy

AA fewfew percentpercent inin thethe earlyearly UniverseUniverse

NotNot possiblepossible forfor aa cosmologicalcosmological constantconstant AA fewfew percentpercent EarlyEarly DarkDark EnergyEnergy

IfIf linearlinear powerpower spectrumspectrum fixedfixed todaytoday (( σσ8 )) ::

MoreMore StructureStructure atat highhigh zz !!

Bartelmann,DoranBartelmann,Doran,,…… EarlyEarly DarkDark EnergyEnergy

AA fewfew percentpercent inin thethe earlyearly UniverseUniverse

NotNot possiblepossible forfor aa cosmologicalcosmological 1σ and 2σ limits constantconstant Doran,Karwan,.. MeasureMeasure ΩΩhh(z(z)) !! HowHow toto distinguishdistinguish QQ fromfrom ΛΛ ??

A)A) MeasurementMeasurement ΩΩh(z(z)) H(zH(z))

i)i) ΩΩh(z(z)) atat thethe timetime ofof structurestructure formationformation ,, CMBCMB -- emissionemission oror nucleosynthesisnucleosynthesis

ii)ii) equationequation ofof statestate wwh((todaytoday)) >> --11

B)B) TimeTime variationvariation ofof fundamentalfundamental ““constantsconstants”” C)C) ApparentApparent violationviolation ofof equivalenceequivalence principleprinciple QuintessenceQuintessence andand timetime variationvariation ofof fundamentalfundamental constantsconstants

Strong, electromagnetic, weak Generic interactions prediction

Strength unknown

C.Wetterich , gravitation cosmodynamics Nucl.Phys.B302,645(1988) TimeTime varyingvarying constantsconstants

„ ItIt isis notnot difficultdifficult toto obtainobtain quintessencequintessence potentialspotentials fromfrom higherhigher dimensionaldimensional oror stringstring theoriestheories „ ExponentialExponential formform ratherrather genericgeneric (( afterafter WeylWeyl scaling)scaling) „ ButBut mostmost modelsmodels showshow tootoo strongstrong timetime dependencedependence ofof constantsconstants !! QuintessenceQuintessence fromfrom higherhigher dimensionsdimensions

workwork withwith J.J. SchwindtSchwindt

hephep--th/0501049th/0501049 QuintessenceQuintessence fromfrom higherhigher dimensionsdimensions

AnAn instructiveinstructive example:example:

EinsteinEinstein –– MaxwellMaxwell theorytheory inin sixsix dimensionsdimensions

WarningWarning :: notnot scalescale -- freefree !! DilatationDilatation anomalyanomaly replacedreplaced byby explicitexplicit massmass scales.scales. MetricMetric AnsatzAnsatz withwith particularparticular metricmetric (( notnot mostmost generalgeneral !! )) whichwhich isis consistentconsistent withwith d=4d=4 homogeneoushomogeneous andand isotropicisotropic UniverseUniverse andand internalinternal U(1)U(1) xx ZZ2 isometryisometry

BB ≠≠ 11 :: footballfootball shapedshaped internalinternal geometrygeometry ExactExact solutionsolution

mm :: monopolemonopole numbernumber (( integer)integer)

cosmologycosmology withwith scalarscalar andand potentialpotential VV :: AsymptoticAsymptotic solutionsolution forfor largelarge tt NaturalnessNaturalness

„ NoNo tuningtuning ofof parametersparameters oror integrationintegration constantsconstants „ RadiationRadiation andand mattermatter cancan bebe implementedimplemented „ AsymptoticAsymptotic solutionsolution dependsdepends onon detailsdetails ofof

model,model, e.g.e.g. solutionssolutions withwith constantconstant ΩΩh ≠≠ 11 problemproblem :: timetime variationvariation ofof fundamentalfundamental constantsconstants AreAre fundamentalfundamental ““constantsconstants”” timetime dependentdependent ??

FineFine structurestructure constantconstant αα (electric(electric charge)charge)

RatioRatio electronelectron toto protonproton massmass

RatioRatio nucleonnucleon massmass toto PlanckPlanck massmass QuintessenceQuintessence andand TimeTime dependencedependence ofof ““fundamentalfundamental constantsconstants””

„ FineFine structurestructure constantconstant dependsdepends onon valuevalue ofof cosmoncosmon fieldfield :: αα((φφ))

(similar(similar inin standardstandard model:model: couplingscouplings dependdepend onon valuevalue ofof HiggsHiggs scalarscalar field)field)

„ TimeTime evolutionevolution ofof φφ TimeTime evolutionevolution ofof αα Jordan,… StandardStandard –– ModelModel ofof electroweakelectroweak interactionsinteractions :: HiggsHiggs -- mechanismmechanism

„ TheThe massesmasses ofof allall fermionsfermions andand gaugegauge bosonsbosons areare proportionalproportional toto thethe (( vacuumvacuum expectationexpectation )) valuevalue ofof aa

scalarscalar fieldfield φφH (( HiggsHiggs scalarscalar )) „ ForFor electron,electron, quarksquarks ,, WW-- andand ZZ-- bosonsbosons ::

mmelectronelectron == hhelectronelectron ** φφHH etc. RestorationRestoration ofof symmetrysymmetry atat highhigh temperaturetemperature inin thethe earlyearly UniverseUniverse

LowLow TT HighHigh TT high T : SSBSSB SYMSYM less order more symmetry <<φφH>=>=φφ0 ≠≠ 00 <<φφH>=0>=0 more symmetry

example: magnets InIn thethe hothot plasmaplasma ofof thethe earlyearly UniverseUniverse ::

NoNo differencedifference inin massmass forfor electronelectron andand muonmuon !! QuintessenceQuintessence :: CouplingsCouplings areare stillstill varyingvarying nownow !!

StrongStrong boundsbounds onon thethe variationvariation ofof couplingscouplings -- interestinginteresting perspectivesperspectives forfor observationobservation !! WhereWhere toto looklook forfor timetime variationvariation ofof fundamentalfundamental couplingscouplings ??

„„ NucleosynthesisNucleosynthesis „„ MolecularMolecular absorptionabsorption lineslines inin thethe lightlight ofof distantdistant QuasarsQuasars „„ OkloOklo naturalnatural reactorreactor „„ AtomicAtomic clocksclocks „„ CMBCMB baryons : the matter of stars and humans

ΩΩbb == 0.0450.045 AbundanciesAbundancies ofof primordialprimordial lightlight elementselements fromfrom nucleosynthesisnucleosynthesis

A.CocA.Coc AllowedAllowed valuesvalues forfor variationvariation ofof finefine structurestructure constantconstant ::

∆α∆α//αα (( z=10z=1010 )) == --1.01.0 1010-3 GUTGUT 11 ∆α∆α//αα (( z=10z=1010 )) == --2.72.7 1010-4 GUTGUT 22

C.Mueller,G.SchaeferC.Mueller,G.Schaefer,,…… Time variation of coupling constants must be tiny –

would be of very high significance !

Possible signal for Quintessence ViolationViolation ofof equivalenceequivalence principleprinciple

DifferentDifferent couplingscouplings ofof cosmoncosmon toto protonproton andand p,n neutronneutron

DifferentialDifferential accelerationacceleration earth cosmon

““ViolationViolation ofof equivalenceequivalence principleprinciple”” p,n

onlyonly apparentapparent :: newnew ““fifthfifth forceforce”” !! ApparentApparent violationviolation ofof equivalenceequivalence principleprinciple

andand

timetime variationvariation ofof fundamentalfundamental couplingscouplings

measuremeasure bothboth thethe

cosmoncosmon –– couplingcoupling toto ordinaryordinary mattermatter DifferentialDifferential accelerationacceleration ηη

ForFor unifiedunified theoriestheories (( GUTGUT )) ::

ηη==∆∆a/2aa/2a

Q : time dependence of other parameters Link between time variation of α

and violation of equivalence principle

typically : η = 10-14

if time variation of α near Oklo upper bound

to be tested by MICROSCOPE SummarySummary oo ΩΩh == 0.750.75 o Q/Q/ΛΛ :: dynamicaldynamical undund staticstatic darkdark energyenergy willwill bebe distinguishabledistinguishable o QQ :: timetime varyingvarying fundamentalfundamental couplingcoupling ““constantsconstants””

violationviolation ofof equivalenceequivalence principleprinciple ????????????????????????????????????????????????

WhyWhy becomesbecomes QuintessenceQuintessence dominantdominant inin thethe presentpresent cosmologicalcosmological epochepoch ?? AreAre darkdark energyenergy andand darkdark mattermatter relatedrelated ?? CanCan QuintessenceQuintessence bebe explainedexplained inin aa fundamentalfundamental unifiedunified theorytheory ?? EndEnd A few references

C.Wetterich , Nucl.Phys.B302,668(1988) , received 24.9.1987

P.J.E.Peebles,B.Ratra , Astrophys.J.Lett.325,L17(1988) , received 20.10.1987

B.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)

P.Ferreira, M.Joyce , Phys.Rev.Lett.79,4740(1997)

C.Wetterich , Astron.Astrophys.301,321(1995)

P.Viana, A.Liddle , Phys.Rev.D57,674(1998)

E.Copeland,A.Liddle,D.Wands , Phys.Rev.D57,4686(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) CosmodynamicsCosmodynamics

CosmonCosmon mediatesmediates newnew longlong--rangerange interactioninteraction Range : size of the Universe – horizon Strength : weaker than gravity photonphoton electrodynamicselectrodynamics gravitongraviton gravitygravity cosmoncosmon cosmodynamicscosmodynamics SmallSmall correctioncorrection toto NewtonNewton’’ss lawlaw TimeTime evolutionevolution ofof fundamentalfundamental couplingscouplings tracestraces timetime evolutionevolution ofof quintessencequintessence

todaytoday wwh closeclose toto --11 ::

•• SmallSmall kinetickinetic energyenergy •• SlowSlow changechange ofof φφ •• SlowSlow changechange ofof αα

VeryVery smallsmall ∆α∆α//αα forfor lowlow zz !! CrossoverCrossover quintessencequintessence andand timetime variationvariation ofof fundamentalfundamental ““constantsconstants””

UpperUpper boundsbounds forfor relativerelative variationvariation ofof thethe finefine structurestructure constantconstant „ OkloOklo naturalnatural reactorreactor ∆∆αα//αα << 1010 -7 z=0.13z=0.13 „ MeteoritesMeteorites (( ReRe--decaydecay )) ∆∆αα//αα << 33 1010 -7 z=0.45z=0.45

„ CrossoverCrossover QuintessenceQuintessence compatiblecompatible withwith QSOQSO andand upperupper boundsbounds !! AtomicAtomic clocksclocks andand OKLOOKLO

assumes that both effects are dominated by change of fine structure constant

ObservationObservation :: ||∆α∆α//αα || << 22 ** 1010 -15 // yryr Munich group VariationVariation ofof finefine structurestructure constantconstant asas functionfunction ofof redshiftredshift

Three independent data sets from Keck/HIRES ∆∆αα//αα == -- 0.540.54 (12)(12) 1010-5

Murphy,Webb,Flammbaum, june 2003

VLT ∆∆αα//αα == -- 0.060.06 (6)(6) 1010-5

Srianand,Chand,Petitjean,Aracil, feb.2004

z ≈ 2 CosmonCosmon andand timetime variationvariation ofof couplingscouplings :: fixedfixed pointspoints

„ smallsmall couplingcoupling ofof cosmoncosmon toto mattermatter duedue toto fixedfixed pointspoints behaviorbehavior

close to fixed point : small time evolution of couplings coupling to matter weaker than gravitational strength FieldField equationsequations EnergyEnergy momentummomentum tensortensor FreeFree integrationintegration constantsconstants

MM ,, BB ,, ΦΦ(t=0)(t=0) ,, (d(dΦΦ//dt)(tdt)(t=0)=0) :: continuouscontinuous mm :: discretediscrete ConicalConical singularitiessingularities deficitdeficit angleangle singularitiessingularities cancan bebe includedincluded withwith energyenergy momentummomentum tensortensor onon branebrane

bulkbulk pointpoint ofof viewview :: describedescribe everythingeverything inin termsterms ofof bulkbulk geometrygeometry (( nono modesmodes onon branebrane withoutwithout tailtail inin bulkbulk )) DimensionalDimensional reductionreduction TimeTime dependentdependent gaugegauge couplingcoupling RealisticRealistic modelmodel :: CrossoverCrossover QuintessenceQuintessence

( like QCD gauge coupling) critical χ where δ grows large critical φ where k grows large k²(φ )=δ(χ)/4

k²(φ )= “1/(2E(φc – φ)/M)” ifif ϕ c ≈ 276/M ( tuning ! )

Relative increase of dark energy in present cosmological epoch