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Quintessencequintessence -- Aa Fifthfifth Forceforce Fromfrom Variationvariation Ofof Thethe Fundamentalfundamental Scalescale Ωωmm ++ XX == 11

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Quintessencequintessence -- Aa Fifthfifth Forceforce Fromfrom Variationvariation Ofof Thethe Fundamentalfundamental Scalescale Ωωmm ++ XX == 11 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
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