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A Simple Model of Large Scale Structure Formation

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arXiv:astro-ph/9310025v1 13 Oct 1993BA-93-53

ASimpleModelofLargeScaleStructureFormation

R.K.SchaeferandQ.Shafi

BartolResearchInstitute

UniversityofDelaware,Newark,DE19716

(February1,2008)

Abstract

Weexploreconstraintsoninflationarymodelsemployingdataonlargescale

structuremainlyfromCOBEtemperatureanisotropiesandIRASselected

galaxysurveys,takingcarenottoapplylinearperturbationtheorytodatain

thenon-linearregime.InmodelswherethetensorcontributiontotheCOBE

signalisnegligible,wefindthespectralindexofdensityfluctuationsnmust

exceed0.7.FurthermoretheCOBEsignalcannotbedominatedbythetensor

component,implyingn>0.85insuchmodels.Thedatafavorscoldplushot

darkmattermodelswithnclosetounityandΩHDM∼0.20−0.35.We

presentrealisticgrandunifiedtheories,includingsupersymmetricversions,

whichproduceinflationwiththeseproperties.98.65Dx,98.80Cq,12.10Dm

TypesetusingREVTEX

1I.INTRODUCTION

Theinflationaryuniversescenario[1]providesanattractiveresolutionofthewellknown“horizon”,“flatness”,and“causality”puzzlesencounteredinthestandardbigbangcos-

mology.Thisscenarioismosteasilyrealizedwithintheframeworkofbothordinaryand

supersymmetricgrandunifiedtheories(GUTS).Inthesimplestrealizationsofinflation,the

densityfluctuationsareGaussianandclosetotheHarrison-Zeldovichform,andtheback-

grounddensityequalsthecriticaldensityρc.Primordialnucleosynthesisimpliesthatless

than10%ofthebackgrounddensityiscomposedofbaryons,andsothebulkofmatteris

“dark”,presumablyintheformofrelicelementaryparticles.

AlmostadecadeagoitwaspointedoutbyShafiandStecker[2]thattwotypesof

darkmatter,coldandhot,wouldprovide,withintheinflationarycontext,anelegantway

ofunderstandingobservationswhichindicatedasurprisingamountofclusteringonlarger

thanclusterscales.Sinceonlythecoldcomponentclusteredonsmallerscales,andthehot

componentonlyclustersonlargerscales,suchauniversewouldhaveanenhancedlarge

scaleclusteringpower.ExamplesofGUTScontainingcoldplushotdarkmatter(C+HDM)

werealsopresented.Theimplicationsofthispictureformicrowavebackgroundanisotropies

wereworkedoutin1989[3,4].Massfunctions[5]bulkstreamingmotions[3,4],cluster

numberdensitiesandcorrelationfunctions,aswellas“greatattractors”werealsofoundto

becompatible[6,7]withdata.

Recentdataonlargescalestructurefromavarietyofsources,particularlyCOBEand

IRASselectedgalaxysurveys,provideadditionalstrongsupporttothisremarkably“simple”

scenarioforstructureformation.TheCOBEgroup[8]foundananisotropyamplitudewhich

theycharacterizedbyanaveragedquadrupolemomentamplitudeδT/T=Qrms−PS/T=

6.2±1.5×10−6.Aswehaveemphasized[9],theearlierpredictions[3,4]forC+HDMmodels

(3/4CDM,1/4HDM)withnegligiblebaryonicmattercontentwere7.8×10−6/b8,whilefor

CDMalonetheyweresignificantlysmaller(4.7×10−6/b),whereb8=(rmsmassfluctuation

onthescale8h−1Mpc)−1.Includinga5%baryondensity(impliedbyprimordialnucleosyn-

2thesis)modifiesthesepredictionsto8.2×10−6/b8forthisC+HDMmixtureand5.1×10−6/b8forCDM.Observationallyderivedvaluesofb8seemtofallintherange1.3

ingtheCOBEresultwasinremarkableagreementwithC+HDMmodels.COBEalsolent

someweaksupportfortheinflationarypowerspectrum;thedataareconsistentwiththe

P(k)∝knspectrumwithn=1.1±0.5[8].FollowingtheCOBEresultotherpiecesofevidencepointingtotheC+HDMmodelwerediscovered:compatibilitywithearlyquasar

formation[10,11],compatibilitywithgalacticcorrelationsandvelocities,[12–14],APMcor-

relations[14,15]quietlocalHubbleflow[16],“cosmicmachnumber”[17],andcountsin

cells[18,19].Thus,thereseemsnodoubtthattheC+HDMmodelisacandidateworthyof

seriousconsideration.

WhileweknowthattheprimordialdensitypowerspectrumP(k)∝kwithC+HDM

providesagoodfittothedata,ithaslongbeenknownthattheinflationaryscenariodoesnot

quiteyieldthissimpleform.Inrecentstudies,thesecorrectionfactorshavebeenexploited

toyieldpowerspectraP(k)∝knwithnsignificantlylessthan1asameanstorepairthe

relativelarge/smallscaleproblemsofthepureCDMmodel.Inthispaper,oneofourtasks

willbetoundertakeastudyoftherangeofallowedn.[Notethatinthisworkwewill

onlyconsidern<∼1,althoughinflationarymodelswherenexceedsunitycanbeconstructed.]

SincewedonotpreciselyknowtheHDMfractionoftheuniverse,wewillexplorethetwo

dimensionalparameterspacen−ΩHDM,andexaminetheconstraintsimposedbythedata.

WedothisbycomparingthemodelpredictionswithdatafromCOBE,thepowerspec-

trumofIRASgalaxies,IRAScounts-incells,andbulkvelocitiesfromthePOTENTanalysis.

Wewillalsoconsiderrequirementsfortheearlyformationofquasars.Afterfittingthenor-

malizationandthebiasfactorforIRASgalaxies,wecalculateχ2foreachmodel.Wethen

comparetheresultsofthemodelsandpresentχ2contourplotsinthen−ΩHDMfraction

plane.WealsoconsiderthepossibilitythatsomeoftheCOBEsignalwasproducedbythe

longwavelengthgravitywavesgeneratedduringinflation.

Becauseofuncertaintiesinthesimulationofstructureformationinthenon-lineargravity

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