Cosmology with a dynamically screened scalar inter

arXiv:hep-th/0407097v112Jul2004hep-th/0407097PUPT-2123CosmologywithadynamicallyscreenedscalarinteractioninthedarksectorStevenS.Gubser∗andP.J.E.Peebles†JosephHenryLaboratories,PrincetonUniversity,Princeton,NJ08544AbstractMotivatedinpartbystringtheory,weconsideramodificationoftheΛCDMcosmologicalmodelinwhichthedarkmatterhasalong-rangescalarforcescreenedbylightparticles.Scalarforcescanhaveinterestingeffectsonstructureformation:themainexamplepresentedhereistheexpulsionofdarkmatterhalosfromlowdensityregions,orvoids,inthegalaxydistribution.February1,2008∗e-mail:[e-mail]†e-mail:[e-mail]1IntroductionWhatiftherewerealong-rangeforceotherthangravityactingonlyonthedarkmatter?Theideaofalong-rangeforcefromtheexchangeofamasslessscalarhasalonghistory,withmorerecentattentiononascalarforceinthedarksectorthatavoidstheconstraintfromtheE¨otv´osexperiment(asreviewedin[1]).AscreeninglengthonadarksectorforcegenerateddynamicallybythepresenceoflightparticleswithaYukawacouplingtothescalarwasdiscussedin[1],andthepictureoftwodarkmatterspecieswithascalarforceofattractionamonglikeparticlesandrepulsionamongunlikeparticleswasdiscussedin[2].Herewecombinethetwonotions,inthedarkmatterlagrangianL=12(∂φ)2+¯Ψsi/∇Ψs+¯Ψ+i/∇Ψ++¯Ψ−i/∇Ψ−−ysφ¯ΨsΨs−(m++y+φ)¯Ψ+Ψ−−(m−−y−φ)¯Ψ−Ψ−.(1)Theconstantsm±andy±areallpositive.ThefermionsΨ±arethenon-relativisticdarkmatter,andthequantaoftheadditionalspeciesΨswillbetermedscreeningparticles.Thescreeningparticlesaremasslessatφ=0,andtheycanprovidedynamicalscreeningbypullingthefieldclosetoφ=0.Anadvantageofthismechanismisthatthescreeninglengthincreaseswiththesizeoftheuniverse,sothatitslengthinco-movingcoordinatesisroughlyconstant:thusitcanplayanimportantroleintheformationandevolutionofthegalaxiesatlowredshiftbutnotsubstantiallyaffecttheformationoftheobservedanisotropyofthe3Kthermalbackgroundradiation(theCMB)atdecouplingatredshiftz∼1000.Wehavetwopurposesinthiscontinuationofourpreviouswork[1,2].First,wecon-tinuetheexplorationofpossibleastrophysicalimplicationsofthescalar-mediatedforcethatemergesfromtheaction(1),inthispaperwithparticularattentiontothepropertiesofvoids.WearguethattherepulsiveforcebetweendarkmatterparticleswithoppositescalarchargecanmakethevoidsmoreemptythanthepredictionoftheΛCDMmodel,andanapparentlybetterapproximationtowhatisobserved[3].Second,wearguethattheac-tion(1)fitsratherneatlyintotheframeworkofsupersymmetryandstringtheory,althoughsupersymmetrybreakingasitisusuallyunderstoodcausessomeproblems.Insummary,wearguethatascalar-mediated,dynamicallyscreenedinteractioninthedarksectorhasboththeoreticalmotivationandpossiblyinterestingobservationalconsequences.InthemodifiedCDMmodelin[2],thedarkmattercouldbedescribedintermsofascalarfieldcoupledtotwospeciesoffermions,withaninteractionlagrangianoftheformLint=−m0eβφ/Mpl¯Ψ1Ψ1−m0e−βφ/Mpl¯Ψ2Ψ2,(2)wherem0isclosetothePlanckscaleandβisoforderunity.Thescalarinteractsonlywiththeseparticles,givingrisetoaninversesquarelawproportionaltotheproductof“scalarcharges”Qi=dmi/dφ.Thetotalscalarchargedensitymustvanishonceφrelaxestoitsequilibriumpoint,determinedbyaneffectivepotentialthatincludescontributionsfromthe1ΦmFigure1:Thesolidlinesdepictthemassesfornon-relativisticdarkmatterspeciesincludedinthemodelof[2].Thedashedlineism(φ)fortheadditional,lightspeciesΨ,whilethegraylineshowsthephysicalmass|m(φ)|.Includingallthreespeciesleadstoamodellike(1),providedφstaysclosetothezeroofm(φ).darkmatter.Additionalspecieswithcouplingstothescalardonotchangethepicturemuch,providedtheyareheavy.Thevariant(1)whichweexploreinthispaperisbasedontheideathatthemassparameterforsomespeciescouldpassthroughzero.Forexample,themasstermforΨsis−ysφ¯ΨsΨs,buttheoverallsignofthistermcanbereversedbyperformingachiralrotation,Ψs→eiπγ5Ψs.Thusfor(1),themassofΨsis|ysφ|.Thesituationissummarizedinfigure1.IftherearemanyΨsquantacomparedtothenumberofΨ±quanta,thenφispinnednearzerobythecontributionofΨstotheeffectivepotential.ThetotalscalarchargeforΨ±quantaneednotbezerobecausethescreeningparticlescanmakeupthedifference—afirsthintthatΨseffectivelyscreensthescalarinteraction.Theorganizationoftheremainderofthepaperisasfollows.Insection2wedescribesomereasonstoregardscalarforcesinthedarksectoraswell-motivatedinstringtheory,andweconstructsupersymmetricgeneralizationsandextensionsoftheaction(1)fromingredientsthatariseincompactificationsofstringtheory.1Insection3webrieflyrecapitulatethedynamicalscreeningmechanism.Aspectsofthegrowthofstructureinthedarkmatterdistribution,inlinearperturbationtheoryandasphericalmodel,arediscussedinsection4,withparticularattentiontothecasewherethetwodarkmatterspecieshaveverydifferentscalarcharge-to-massratios.Insection4.3weconsiderthepossibleapplicationtothepropertiesofvoidsinthedistributionofnormalgalaxies.2SupersymmetricandstringtheoreticmodelsTherearebothtop-downandbottom-upmotivationstoconsideralinkbetweenstringtheoryandscalarforcesinthedarksector.1Thereaderwishingtopasslightlyoverthestringtheorymayfindthesummaryinsubsection2.5helpful.2Atop-downmotivationisthattherearemoduliinstringtheory,andthereareheavyob-