Large scale structure formation in mixed dark matt

arXiv:astro-ph/9804057v16Apr1998A&Amanuscriptno.(willbeinsertedbyhandlater)Yourthesauruscodesare:(12.03.4;12.04.1;12.12.1;Universe11.03.1;ASTRONOMYANDASTROPHYSICS1.2.2008LargescalestructureformationinmixeddarkmattermodelswithacosmologicalconstantR.Valdarnini1,T.Kahniashvili2,B.Novosyadlyj31SISSA,viaBeirut2-4,34014,Trieste,Italy2AbastumaniAstrophysicalObservatory,A.Kazbegiave.2a,380060,Tbilisi,Georgia3AstronomicalObservatoryofL’vivStateUniversity,KyrylaandMephodiastr.8,290005,L’viv,UkraineReceived...;accepted...Abstract.WestudylinearpowerspectraandformationoflargescalestructuresinflatcosmologicalmodelswithΛ≥0andcoldplushotdarkmattercomponents.Were-fertothesemodelsasmixedΛmodels(MLM).Thehotcomponentconsistsofmassiveneutrinoswithcosmologi-caldensityΩHandnumberofneutrinospeciesasafreepa-rameter.ThelinearizedEinstein-Boltzmannequationsfortheevolutionofthemetricanddensityperturbationsareintegratedforasetofvaluesofthecosmologicalparame-ters.WestudyMLMmodelswithpresentmatterdensityintherange0.25≤ΩM≤1,dimensionlessHubblecon-stant0.4≤h≤0.7andthehotdarkmattercontentwitharatiowithinthelimits0≤ΩH/ΩM≤0.3.Foralltheconsideredmodelsweassumeascale-invariantprimevalspectrum.ThedensityweightedfinallinearpowerspectraarenormalizedtothefouryearCOBEdataandhavebeenusedtoconstraintheparameterspacebyacomparisonoflinearpredictionswiththecurrentobservationaldataonlargescales.TheconsistencyofMLMpredictionswiththeobservabledatasetisbestobtainedformodelswithonespeciesofmassiveneutrinosandΩH/ΩM≤0.2.OftheconsideredlinearteststhestrongestconstraintsonΩMthatweobtainarisebycomparingtheclusterX-raytemperaturefunctionwiththatobservedatthepresentepoch.ConsistencywiththeestimatedclusterabundancecanbeachievedforCOBEnormalizedMLMmodelswithΩH/ΩM≤0.2and0.45≤ΩM≤0.75forh=0.5.Ifh=0.7then0.3≤ΩM≤0.5.Theseconstraintsareat1σlevelandstandardMDMmodelsareclearlyruledout.WenotethattherangeofallowedvaluesforΩM,thatweobtainforMLMmodelsfromlinearanalysis,isalsoapproximatelythesamerangethatisneededinordertoconsistentlysatisfyavarietyofindependentobservationalconstraints.Sendoffprintrequeststo:RiccardoValdarniniKeywords:mixeddarkmatter–large-scalestructure–cosmologicalconstant1.IntroductionInthestandardframeworkofgravitationalinstabilitythe-orypresentdaystructuresmusthavebeenformedthroughthegrowthofsmallinhomogeneitiesfromaninitialran-domGaussiandensityfieldpresentatveryearlyepochs,withascale-invariantHarrison-Zel’dovichspectrum.Clus-teringanalysisofthelargescalestructureintheUniversehasbeenimprovedinrecentyearsbyobservationsofthespatialdistributionofgalaxiesandclusterofgalaxies,aswellascosmicmicrowavebackground(CMB)anisotropies.Thusanytheorythatwantstofittheobservedlargescaleclusteringmustbeconsistentwithasetofconstraintsovermorethanthreedecadesinlength:fromgalaxycor-relation(∼1h−1Mpc,H0=100hKmsec−1Mpc−1)uptothequadrupoleCMBanisotropiesdetectedbyCOBE(∼3000h−1Mpc,Smootetal.1992).InthestandardFRWmetricthefundamentalback-groundcosmologicalparametersarerelatedbyamutualrelation.Itisalsounderstoodthatfortheseparame-ters(thepresentmatterdensityΩM,thevalueoftheHubbleconstantH0andtheageoftheuniverset0)therangeofvaluesallowedbyobservationsmustbeconsis-tentwiththeirFRWrelation.IfweadoptthestandardinflationtheoryweshallassumethatthetotalenergydensityintheUniverseisequaltothecriticaldensity(Ω0=1).Ontheotherhand,observationsandtheoreti-calpredictionssuggestthattheamountofbaryondensitymustbesmall(Ωb∼0.05(h/0.5)−2,Walkeretal.1991,Copi,Schramm&Turner1995).Amuchlargercontribu-tiontothematterdensitymustbeofnon-baryonicnature.Thisisso-calleddarkmatter(DM)problemandithasobservationalsupportfromdynamicalestimates(ΩM∼2MixedDarkMatterModelswithaCosmologicalConstant0.2−0.3,Bahcall1996andreferencescitedtherein).ItmustbestressedthatthereisnotyetafirmevidenceforΩM=1,thisvalueforΩMbeingrequiredbytheinflation-aryparadigm.ThesimplestpossiblemodelofDMistheoneinwhichtheuniverseisdynamicallydominatedbyasinglemassivecollisionlessparticle.ThemostpopularDMcandidatesarecollisionlessmassiveparticles,whichdecoupledfromcosmologicalplasmaeitherwhenbeingrel-ativistic(DMparticleslikemassiveneutrinos–HotDM)ornon-relativistic(hypotheticalmassiveparticles–ColdDM).ThesimplestmodelisCDM,wherethepowerspec-trumoftheperturbationsdependsonasingleparam-eter,thepresentcolddensityΩC.Historicallythefirstmodeltobeconsideredwasaneutrinowithanon-zerorestmassHDM(Bond&Szalay1983;Zakharov1979).TheHDMmodelwassoonrejectedbecausenu-mericalsimulations(White,Frenk&Davis1983)pro-ducednonlinearstructurestoolatetobeinagree-mentwithQSOexistence.ThestandardCDMmodel(SCDM)hasbeenanalysedinconsiderabledetails(Davisetal.1985;Davis&Efstathiou1988andrefer-encescitedtherein).Itcanmatchgalaxycluster-ing(∼10h−1Mpc)withabiasparameterbg∼2,al-thoughitlacksofsufficientpoweronlargescales.TheSCDMmodelhoweverbecameseriouslyinconsis-tentwithclusteringdataaftertheCOBEdetectionofaquadrupoleanisotropyintheCMB(Smootetal.1992).Whenthepowerspectrumofthemodelisnormal-izedtotheCOBEdataSCDMmodelshaveun-avoidabledifficulties(White,Efstathiou&Frenk1993a;Olivieretal.1993;Mo,Ji