The Future of the Local Large Scale Structure the

arXiv:0705.4477v2[astro-ph]10Oct2007TheFutureoftheLocalLargeScaleStructure:therolesofDarkMatterandDarkEnergyYehudaHoffman1,OferLahav2,GustavoYepes3,andYanivDover11RacahInstituteofPhysics,HebrewUniversity,Jerusalem91904,Israel2DepartmentofPhysicsandAstronomy,UniversityCollegeLondon,GowerStreet,LondonWC1E6BT,UK3GrupodeAstrof´ısica,UniversidadAut´onomadeMadrid,MadridE-280049,SpainAbstract.WestudythedistincteffectsofDarkMatterandDarkEnergyonthefutureevolutionofnearbylargescalestructuresusingconstrainedN-bodysimulations.WecontrastamodelofColdDarkMatterandaCosmologicalConstant(ΛCDM)withanOpenCDM(OCDM)modelwiththesamematterdensityΩm=0.3andthesameHubbleconstanth=0.7.Alreadybythetimethescalefactorincreasedbyafactorof6(29GyrfromnowinΛCDM;78GyrfromnowinOCDM)thecomovingpositionoftheLocalGroupisfrozen.WellbeforethatepochthetwomostmassivemembersoftheLocalGroup,theMilkyWayandAndromeda,willmerge.However,astheexpansionratesofthescalefactorinthetwomodelsaredifferent,theLocalGroupwillberecedinginphysicalcoordinatesfromVirgoexponentiallyinaΛCDMmodelandataroughlyconstantvelocityinanOCDMmodel.Moregenerally,incomovingcoordinatesthefuturelargescalestructurewilllooklikeasharpenedimageofthepresentstructure:theskeletonofthecosmicwebwillremainthesame,butclusterswillbemore‘isolated’andthefilamentswillbecomethinner.Thisimpliesthatthelong-termfateoflargescalestructureasseenincomovingcoordinatesisdeterminedprimarilybythematterdensity.WeconcludethatalthoughtheΛCDMmodelisacceleratingatpresentduetoitsDarkEnergycomponentwhiletheOCDMmodelisnonaccelerating,theirlargescalestructureinthefuturewilllookverysimilarincomovingcoordinates.Submittedto:AceptedforpublicationinJCAPTheFutureoftheLocalLargeScaleStructure21.IntroductionCosmologistsusuallystudythepastevolutionoftheuniverse.Indeed,theLocalUniversehasbeenusedbeforeasalaboratoryforstudyingdynamicsandcosmologicalparameters,forexamplethetimingargument(Raychaudhury&Lynden-Bell1989,Karachentsev2005),orN-bodymethods(Peeblesetal.,1989).Similarly,wecangaininsightintothedynamicsandtheroleoftheDarkMatterandDarkEnergycomponentsoftheuniversebyconsideringthefutureevolutionofnearbylargescalestructure.Thebackgroundcosmologyisnowreasonablywellestablishedbasedonthemeasurementsofthecosmicmicrowavebackground,thelargeredshiftsurveys,SupernovaeIadataandotherprobes(e.g.Spergeletal.2006andreferencestherein).Thesemeasurementssupporta‘concordance’modelinwhichtheuniverseisflatandcontainsapproximately4%baryons,21%ColdDarkMatterand75%DarkEnergy,withapossiblesmallcontributionofmassiveneutrinos.ThenatureoftheDarkMatterandtheDarkEnergyarestilltobeunderstood,inparticularthepossibilityofamoregeneralequationofstateoftheDarkEnergycomponent,w=P/ρ,whichmightalsobeevolvingwithcosmicepoch.Thecasew=−1correspondstoEinstein’sCosmologicalConstantΛ,whichweshallconsiderinthispaper,asitisconsistentwiththecurrentobservations.WeshallrefertothismodelasΛColdDarkMatter(ΛCDM).ThefateofaΛCDMuniverseasawholehasbeendiscussedbefore(e.g.Loeb,2002;Krauss&Scherrer,2007).ThegoalofthepresentstudyistocontrasttheΛCDMmodelwithanOCDMmodelwiththesamematterdensityparameter,toinvestigatetherolesoftheDarkMatterandtheDarkEnergyintheevolutionofclustering.WhentheuniversewillbecompletelydominatedbytheΛtermthescalefactorwillexpandexponentially,a(t)∝exp(qΛ/3t)(a‘de-Sitterphase’).Itislessclearwhatwillhappentothegrowthofstructureandtoindividualobjectsintheuniverse.e.g.willtheymanagetosurviveasboundobjectsinanexponentiallyexpandinguniverse?PapersbyNagamine&Loeb(2003,hereafterNL03)andBushaetal.(2005)havealreadyconsideredsomeofthesequestions.InparticularNL03usedaconstrainedN-bodysimulationforaΛCDMuniversetopredictthefutureevolutionofnearbylargescalestructure.Theyfoundthatstructureswillfreezeincomovingcoordinates.Inparticulartheyfoundthat“theLocalGroupwillgetsomewhatclosertotheVirgoclusterincomovingcoordinates,butwillbepulledawayfromVirgoinphysicalcoordinatesduetotheacceleratedexpansionoftheuniverse.”However,oneshouldrecallthatthefreezeoutofthegrowthofstructureisnotthesignatureofthecosmologicalconstantbutratherofthefactthatthedensityofmatterislessthanthecritical.Namely,inauniversedominatedeitherbythenegativecurvatureorbytheΛtermgravitationalinstabilitystalls.Thelineartheorygrowthofdensityperturbationsinauniversewithandwithoutacosmologicalconstantisillustratedinnumerouspapers(e.g.Figure2of(Lahav&Suto,2004)).ThishasmotivatedustoexplorethefateoftheuniverseinthegeneralcasewherethemeanmatterdensityissubcriticalandcomparethecasesofaΛdominateduniversewithanTheFutureoftheLocalLargeScaleStructure3openone.HereweextendtheNL03studytoexploretowhatextentthisfateofthelocalstructuredependsontheDarkMatterandDarkEnergycontentsoftheuniverse.WeusethetoolofConstrainedRealizationsofGaussianrandomfields(Hoffman&Ribak,1991)toconstraintheinitialconditionsfortheN-bodysimulationsbyobservationaldata.TheresultingsimulationsreproducequitefaithfullytheobservedLSSouttoafewtensofMpcfromtheLG.WeapplythesimulationstobothΛCDMmodelandanOpenColdDarkMatter(OCDM)modelwiththesameΩm=0.3andthesameHubbleconstanth=0.7.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