Cosmological Acceleration Dark Energy or Modified

arXiv:astro-ph/0605198v212Jun2006COSMOLOGICALACCELERATION:DARKENERGYORMODIFIEDGRAVITY?SidneyBludman∗DESY,22607Hamburg,Germany(Dated:February5,2008)Therecentlyobservedacceleratingcosmologicalexpansionor”darkenergy”maybeeitheranegativepressureconstituentinGeneralRelativity(DarkEnergy)ormodifiedgravity(DarkGravity)withoutanyconstituentDarkEnergy.Low-orhigh-curvaturemodificationsofEinsteingravityaredistinguishedbythespacetime(Ricci)curvatureoftheirvacua.IfconstituentDarkEnergydoesnotexist,sothatouruniverseisnowdominatedbypressure-freematter,Einsteingravitymustbemodifiedatlow-curvature,becomingasymptoticallydeSitter.Thedynamicsofeitherkindof”darkenergy”cannotbederivedfromthehomogeneousexpansionhistoryalone,butrequiresalsoobservingthegrowthofinhomogeneities.Presentandprojectedobservationsareallconsistentwithasmallfine-tunedcosmologicalconstant,butalsoallownearlystaticDarkEnergyorgravitymodifiedatcosmologicalscales.Thegrowthofcosmologicalfluctua-tionswillpotentiallydistinguishbetweenstaticand”dynamic”darkenergy”.But,cosmologicallydistinguishingdynamicDarkEnergyfromDarkGravitywillrequireaweaklensingshearsurveymoreambitiousthananynowprojected.Dvali-Gabadadze-Porratilow-curvaturemodificationsofEinsteingravitymayalsobedetectedinrefinedobservationsinthesolarsystemorinisolatedgalaxyclusters.WereviewlocalandcosmologicaltestsofGeneralRelativityandmodifiedgravity.DarkEnergyisepicyclicincharacter,requiresfine-tuningtoexplainwhyitsenergydensityisjustnowcomparabletoordinarymatterdensity,andcannotbedetectedinthelaboratoryorsolarsystem.This,alongwithbraneworldtheories,nowmotivatesearchingforDarkGravityonsolarsystem,galaxyclusterandcosmologicalscales.ContentsI.INTRODUCTION:COSMOLOGICALSYMMETRYVS.DYNAMICS2II.EXPANSIONHISTORYH(z)INROBERTSON-WALKERCOSMOLOGIES3A.Kinematics:DistancestoSupernovae,LuminousRedGalaxies,LastScatteringSurface3B.ExpansionHistoryDoesNotDetermineCosmodynamics4III.CLASSIFICATIONOFROBERTSON-WALKERCOSMOLOGIESBYTHEIRVACUUMSYMMETRY6A.HomogeneousEvolutionConventionallyDescribedbyGeneralRelativityPerfectFluids6B.DarkEnergyRequiresFineTuningtoExplaintheCosmicCoincidence8C.WithoutDarkEnergy,OurUniverseMustBeAsymptoticallydeSitter8IV.DYNAMICSDETERMINESTHEGROWTHOFFLUCTUATIONS9V.DARKGRAVITY:DYNAMICALMODIFICATIONSOFGENERALRELATIVITY9A.PresentLocalandCosmologicalTestsofGeneralRelativity9B.ClassificationofModifiedGravityTheoriesbySpacetimeCurvatureofTheirVacuua101.ExtraDegreesofFreedominFour-DimensionalGravity102.ExtraDimensionalModificationsofEinsteinGravity11C.ProspectiveTestsofModifiedGravity14VI.CONCLUSIONS:ΛCDM,FINE-TUNEDDARKENERGY,ORMODIFIEDGRAVITY14Acknowledgments14References15∗Electronicaddress:[e-mail];URL:~bludman2I.INTRODUCTION:COSMOLOGICALSYMMETRYVS.DYNAMICSThegreatestmysteryincosmologyisthe“darkenergy”sourceofthelate(redshiftz.1/2)cosmologicalaccel-eration.This“darkenergy”maybestaticordynamicandeitheranadditionalnegative-pressurematterconstituentwithinGeneralRelativity(DarkEnergy),oramodificationofGeneralRelativity(DarkGravity(GuandHwang,2002)).Thisreviewrestsontheobservedglobalhomogeneityandisotropyoftheuniverse(Robertson-Walkercos-mologyRW),andwillemphasizethedifferencebetweenRobertson-Walkerkinematicsanddynamics.WewillrecallwhenRWsymmetrycoulddeterminethecosmodynamics:ToexplaintheobservedpresentcosmologicalaccelerationwithoutconstituentDarkEnergy,Einsteindynamicsmustbemodifiedatlowspacetime(Ricci)curvature.BecausethehomogeneousexpansionhistoryH(z)oftheglobaluniversemeasuresonlykinematicvariables,itcannotfixtheunderlyingdynamics:cosmographicmeasurementsofthelateacceleratinguniverse,areconsistentwitheitherastaticcosmologicalconstantoradynamic“darkenergy”,whichitselfmaybeconstituentDarkEnergyormodifiedgravity(DarkGravity).TheConcordanceModelΛCDM,withasmallstaticDarkEnergyorcosmologicalconstantΛ,givesagoodfittoallpresentobservations,butalsoallowsamoderatelydynamic“darkenergy”(Spergeletal.,2006).Wewillreviewhowstaticanddynamic“darkenergy”andhowdynamicDarkEnergyandDarkGravitycouldbedistinguishedtheoreticallyandbyfuturecosmological,localorintermediatescaleobservations.WhetherDarkEnergyorDarkGravity,“darkenergy”hastwodistinctdynamicaleffects:italtersthehomogeneousexpansionhistoryH(z)anditsuppressesthegrowthofdensityfluctuationsδatlargecosmologicalscalea(t).Becausethegrowthfunctiong(z)≡δ/adependsonboththeseeffects,largeangularscaleCMBtemperatureanisotropies,thelate-timegrowthoflargescalestructure,andrefinedweaklensingobservationspotentiallydistinguishstaticfromdynamic”darkenergy”andDarkEnergyfromDarkGravity(SectionII).Inanymetrictheoryofgravitation,thematerialstress-energysourcesTμνdeterminesthespacetime(Ricci)cur-vaturetensorRμνorEinsteincurvaturetensorGμν≡Rμν−gμνR/2.Beforeconsideringdynamicalalternatives,werecallhowtheasymptoticspacetimecurvature,atvanishingmatterdensity,canconstrainanyRWdynamics,withoutassumingEinsteingravity:Birkhoff’sTheoremisageometrictheorem,holdinginanysphericallysymmetricmet-ricgeometrywhosevacuumhasvanishingspacetime(Ricci)scalarcurvature(C.CallanandPeebles,1965;Peebles,1980).Appliedt