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arXiv:astro-ph/0703303v218Jun2007LimitsoncouplingbetweendarkcomponentsRobertoMainini,SilvioBonomettoDepartmentofPhysicsG.Occhialini–Milano–BicoccaUniversity,PiazzadellaScienza3,20126Milano,Italy&I.N.F.N.,SezionediMilanoAbstract.DM–DEcouplingcanbeaphenomenologicalindicationofacommonoriginofthedarkcosmiccomponents.Inthisworkweoutlineanewconstrainttocoupled–DEmodels:thecouplingcanpartiallyortotallysuppresstheMeszaroseffect,yieldingtransferedspectrawithquiteasoftbendingabovekhor,eq.ModelsaffectedbythisanomalydonotshowmajorvariationintheCMBanisotropyspectrumanditishereforehardtoreconcilethemwithbothCMBanddeepsampledata,throughthesamevalueoftheprimevalspectralindex.PACSnumbers:98.80.-k,98.65.-rLimitsoncouplingbetweendarkcomponents21.IntroductionTherecanbelittledoubtsthatatenablecosmologicalmodelmustincludeatleasttwodarkcomponents,coldDarkMatter(DM)andDarkEnergy(DE);yetonlyhypothesesontheirnatureexist,mostofthemassumingthatDMandDEarephysicallyunrelatedandthattheirsimilardensities,intoday’sworldandjustinit,arepurelyaccidental.Attemptstoovercomethisconceptualdeadlockweremadebyseveralauthorssuggesting,firstofall,thatDEhasadynamicalnature[1](forareviewsee[2]andreferencestherein).AnalternativeideaisthatDEisaphenomenologicalconsequenceoftheemergenceofnonlinearity;thisappealingoptionwasrepeatedlyconsidered(see,e.g.,[3]andreferencestherein),butisfarfrombeingshownandleaveshoweverapartthequestionofDMnature.InteractionsbetweenDManddynamicalDE[4](seealso[5])mightpartiallycuretheproblem,keepingclosevaluesfortheirdensitiesuptolargeredshift.Thisoptioncouldalsobereadasanapproachtoadeeperreality,whosephysicalfeaturescouldemergefromphenomenologicallimitstocouplingstrengthandshape.Alongerstepforwardwasattemptedby[6],suggestingthatDMandDEderivefromasinglecomplexscalarfield,beingitsquantizedphaseandmodulus,respectively.ThecomplexfieldcouldbetheoneresponsibleforCPconservationinstronginteractions,withinaschemesimilartoPeccei&Quinnframework[7](seealso[8]).Atvariancefromprevioussuggestions,whichintroduceparametersandaimatlimitingthemthroughdatafitting,thisoption–dubbeddual–axionmodel–cutstheavailabledegreesoffreedom,includingasmanyparametersasastandard–CDMapproach.Itisthenquiteappealingthatitsreducedparameterbudgetissufficienttofitquiteanumberofobservationalconstraints[9],stillallowingforacommonnatureofDMandDEandforaspecificshapeofinteractionbetweenthem.Inthispaper,however,wekeeponthephenomenologicalsideanddiscussgenericconstraintstoDM–DEinteractions.Thisdiscussionwillhaveafalloutalsoonthedual–axionapproach,whichdoesfaceaproblem,becauseofthefeatureoftheDM–DEcouplingitcauses.AcouplingofbaryonswithDEisruledoutbyobservationalconsequencessimilartomodifyinggravity.LimitsarelooserforDM–DEcoupling,whoseconsequencescanbeappreciatedonlyovercosmologicaldistances.ItshouldalsobeoutlinedthatforcesactingwithinthedarksectorcouldmodifypredictionsonhighconcentrationDMlumps.TherecanbelittledoubtsthatcoldDMparticles,feelinggravityonly,givethemNFWprofiles.Yet,observationaldatadonotlendmuchsupporttothisshape,foranyscalerange,anddirectinteractionbetweenDMparticlesisseverelyconstrainedalsobyrecentdata.ThisisafurtherreasontoconsiderDM–DEinteractions,eitherasafundamentaltheoryorasaneffectiveframeworktoapproachdeeperphysics.Itisthenimportanttodeviseanyobservationallimittosuchinteractionsand,inthispaper,weoutlinefurtherconstraintstoitsshape;theyareconsequencesoftheearlybehaviorofdensityLimitsoncouplingbetweendarkcomponents3fluctuations,overscalesdestinedtoevolveintonon–linearstructures.Fluctuationsoversuchscalesenterthehorizonbeforematter–radiationequalityandtheirgrowthisinitiallyinhibitedbytheoverwhelmingdensityoftheradiativecomponent,thenstillbehavingasasinglefluidtogetherwithbaryons.Whilefluctuationsinthefluidbehaveassonicwaves,selfgravitationofDMisjustaminordynamicaleffectisrespecttocosmicexpansion.ThisfreezingoffluctuationamplitudesuntilequalityisknownasMeszaroseffect.ThemainpointwewishtooutlinehereisthatDM–DEcouplingcandampMeszaroseffect,sothattherateoffluctuationgrowth,betweentheentryinthehorizonandequality,issignificantlyenhanced.Asamatteroffact,fluctuationfreezingisessential,inshapingthetransferedspectrum,whichpeaksonthescalekhor,eqenteringthehorizonatequality.Atsmallermassscales(kkhor,eq)thespectrumdeclinesbecauseoftheincreasingdurationofthefreeze.Thefreezingoritsdampinghavemodestconsequencesontheevolutionoffluctuationsinbaryonsandradiation,evolvingtheninthesonicregime.Whatweshallthereforefindaresignificantchangesinthetransferfuncions,whileCMBspectrakeepalmostunaffected.ConstraintstocoupledDEmodelsarisefrombothlinearandnon–lineareffects.Ithasbeenknownsincelongthatcouplingmaycauseaφ–MDepochaftermatter–radiationequality(see,e.g.,[10]).Thischangesthe(comoving)distanceofthelastscatteringband.Inordertofitdata,thepresentvalueoftheHubbleparameterHoneedsthentobeincreased.LimitsonHoturnthenintolimitstothecoupling.Limitstothecoupling,inthecaseofaRatraPeebles[11]self–interactionpotential,wherealsofoundin[12],bystudyinghaloconcentrationdistibution.Thefeatureoutlinedinthisworkaffectsthetransferfu