Emergent gravity and Dark Energy

arXiv:0802.1798v1[gr-qc]13Feb2008EmergentgravityandDarkEnergyT.PadmanabhanIUCAA,PuneUniversityCampus,Ganeshkhind,Pune411007,INDIAemail:[e-mail]1TheriseoftheDarkEnergyGiventheexpansionrateoftheuniverseintermsoftheHubbleconstantH0=(˙a/a)0,onecandefineacriticalenergydensityρc=3H20/8πGwhichisrequiredtomakethespatialsectionsoftheuniversecompact.Itisconvenienttomeasuretheenergydensitiesofthedifferentspecies,whichdrivetheexpansionoftheuniverse,intermsofthiscriticaldensityusingthedimensionlessparametersΩi=ρi/ρc(withidenotingthedifferentcomponentslikebaryons,darkmatter,radiation,etc.)Thesimplestpossibleuniverseonecouldimaginewouldhavejustbaryonsandradiation.However,hostofastronomicalobservationsavailablesincemid-70sindicatedthatthebulkofthematterintheuniverseisnonbaryonicanddark.Aroundthesametime,thetheoreticalprejudiceforΩtot=1gainedmomentum,largelyledbytheinflationaryparadigm.Duringtheeighties,thisledmanytheoreticianstopush(wrongly!)foramodelofthewithΩtot≈ΩDM≈1inspiteofthefactthathostofastronomicalobservationsdemandedthatΩDM≃0.2−0.3.Theindicationsthattheuniverseindeedhasanothercomponentofenergydensitystartedaccumulatinginthelateeightiesandearlynineties.Earlyanal-ysisofseveralobservations[1]indicatedthatthiscomponentisunclusteredandhasnegativepressure.Thisisconfirmeddramaticallybythesupernovaob-servationsinthelatenineties(seeRef.[2];foracriticallookatthecurrentdata,seeRef.[3]).Theobservationssuggestthatthemissingcomponenthasw=p/ρ.−0.78andcontributesΩDE∼=0.60−0.75.Thesimplestchoiceforsuchdarkenergywithnegativepressureisthecos-mologicalconstantwhichisatermthatcanbeaddedtoEinstein’sequations.ThistermactslikeafluidwithanequationofstatepDE=−ρDE.Combiningthiswithallotherobservations[4,5,6],weendupwithaweirdcompositionfortheuniversewith0.98.Ωtot.1.08inwhichradiation(R),baryons(B),darkmatter,madeofweaklyinteractingmassiveparticles(DM)anddarken-ergy(DE)contributesΩR≃5×10−5,ΩB≃0.04,ΩDM≃0.26,ΩDE≃0.7,respectively.Sothebulkoftheenergydensityintheuniverseiscontributedbydarkenergy,whichisthemeofthisarticle.Theremarkablysuccessfulparadigmofconventionalcosmologyisbasedon1thesenumbersandworks[7]asfollows:Thekeyideaisthatifthereexistedsmallfluctuationsintheenergydensityintheearlyuniverse,thengravitationalinstabilitycanamplifythemleadingtostructureslikegalaxiesetc.today.Thepopularprocedureforgeneratingthesefluctuationsisbasedontheideathatiftheveryearlyuniversewentthroughaninflationaryphase[8],thenthequan-tumfluctuationsofthefielddrivingtheinflationcanleadtoenergydensityfluctuations[9,10].Whiletheinflationarymodelsarefarfromuniqueandhencelackspredictivepower,itiscertainlypossibletoconstructmodelsofin-flationsuchthatthesefluctuationsaredescribedbyaGaussianrandomfieldandarecharacterizedbyapowerspectrumoftheformP(k)=Aknwithn≃1.TheinflationarymodelscannotpredictthevalueoftheamplitudeAinanun-ambiguousmanner.ButitcanbedeterminedfromCMBRobservationsandtheinflationarymodelparameterscanbefine-tunedtoreproducetheobservedvalue.TheCMBRobservationsareconsistentwiththeinflationarymodelforthegenerationofperturbationsandgivesA≃(28.3h−1Mpc)4andn.1.(ThefirstresultswerefromCOBE[11]andWMAPhasre-confirmedthemwithfargreateraccuracy).Onecanevolvetheinitialperturbationsbylinearperturba-tiontheorywhentheperturbationissmall.Butwhenδ≈(δρ/ρ)iscomparabletounitytheperturbationtheorybreaksdownandonehastoresorttonumeri-calsimulations[12]ortheoreticalmodelsbasedonapproximateansatz[13,14]tounderstandtheirevolution—especiallythebaryonicpart,thatleadstoob-servedstructuresintheuniverse.Thisrapidsummaryshowsthatmodelingtheuniverseandcomparingthetheorywithobservationsisaratherinvolvedaffair;buttheresultsobtainedfromalltheseattemptsarebroadlyconsistentwithobservations.Tothezerothorder,theuniverseischaracterizedbyjustsevennumbers:h≈0.7describingthecurrentrateofexpansion;ΩDE≃0.7,ΩDM≃0.26,ΩB≃0.04,ΩR≃5×10−5givingthecompositionoftheuniverse;theamplitudeA≃(28.3h−1Mpc)4andtheindexn≃1oftheinitialperturbations.2AfirstlookatcosmologicalconstantanditsproblemsTheremainingchallenge,ofcourse,istomakesomesenseoutofthesenumbersthemselvesfromamorefundamentalpointofview.Amongallthesecompo-nents,thedarkenergy,whichexertsnegativepressure,isprobablytheweirdestoneandhasattractedmostoftheattention.Thekeyobservationalfeatureofdarkenergyisthat,whentreatedasafluidwithastresstensorTab=dia(ρ,−p,−p,−p),ithasanequationstatep=wρwithw.−0.8atthepresentepoch.Thespatialpartgofthegeodesicacceleration(whichmeasurestherelativeaccelerationoftwogeodesicsinthespacetime)satisfiesanexactequationingeneralrelativitygivenby:∇·g=−4πG(ρ+3p)(1)2Thisshowsthatthesourceofgeodesicaccelerationis(ρ+3p)andnotρ.Aslongas(ρ+3p)0,gravityremainsattractivewhile(ρ+3p)0canleadto‘repul-sive’gravitationaleffects.Inotherwords,darkenergywithsufficientlynegativepressurewillacceleratetheexpansionoftheuniverse,onceitstartsdominatingoverthenormalmatter.Thisispreciselywhatisestablishedfromthestudyofhighredshiftsupernova,whichcanbeusedtodeterminetheexpansionrateoftheuniverseinthepast[2,15].Thesimplestmodelforafluidwithnegativepressureisnotafluidatallbutthecosmolog