Dark Energy and Dark Matter in Galaxy Halos

We consider the possibility that the dark matter is coupled through its mass to a scalar field associated with the dark energy of the Universe. In order for such a field to play a role at the present cosmological distances, it must be effectively massless

DarkEnergyandDarkMatterinGalaxyHalos

arXiv:hep-ph/0507288v2 23 Sep 2005N.TetradisUniversityofAthens,DepartmentofPhysics,UniversityCampus,Zographou15784,Athens,Greece.AbstractWeconsiderthepossibilitythatthedarkmatteriscoupledthroughitsmasstoascalar eldassociatedwiththedarkenergyoftheUniverse.Inorderforsucha eldtoplayaroleatthepresentcosmologicaldistances,itmustbee ectivelymasslessatgalacticlengthscales.Wediscussthee ectofthe eldonthedistributionofdarkmatteringalaxyhalos.Weshowthatthepro leofthedistributionoutsidethegalaxycoreremainslargelyuna ectedandtheapproximately atrotationcurvespersist.Thedispersionofthedarkmattervelocityisenhancedbyapotentiallylargefactorrelativetothecaseofzerocouplingbetweendarkenergyanddarkmatter.Thecountingratesinterrestrialdarkmatterdetectorsaresimilarlyenhanced.Existingboundsonthepropertiesofdarkmattercandidatescanbeextendedtothecoupledcase,bytakingintoaccounttheenhancementfactor.PACSnumbers:95.35.+d,98.35.Gi,98.80.Cq

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We consider the possibility that the dark matter is coupled through its mass to a scalar field associated with the dark energy of the Universe. In order for such a field to play a role at the present cosmological distances, it must be effectively massless

AccordingtoourpresentunderstandingofthemattercontentoftheUniverse,itsenergydensityisdominatedbydarkenergyanddarkmatter.Theusualassumptionisthatthedarkenergyisassociatedwiththepotentialofanevolvingscalar eld[1,2],http://doc.guandang.netuallythesetwosectorsareassumedtointeractonlygravitationally.Attemptstoresolvethecoincidenceproblem(thecomparablepresentcontributionstothetotalenergydensityfromthetwocomponents)arebasedonthepresenceofanadditionalinteractionbetweenthedarkmatterandthescalar eld[3].Thecosmologicalevolutionnowdependsonthepotentialofthe eld,aswellasonthetypeandstrengthoftheinteraction[4].Forascalar eldtoberelevantforthecosmologicalevolutiontoday,soastoresolvethecoincidenceproblem,thescaleforitse ectivemassmustbesetbythepresentvalueoftheHubbleparameter[3].Thismeansthatthe eldise ectivelymasslessatgalacticlengthscales.Itscouplingtothedarkmatterparticlesresultsinalong-rangeforcethatcana ectthedetailsofstructureformation[5,6].

Thepresenceofalong-rangescalarinteractioninadditiontogravitycanmodifythedis-tributionofdarkmatteringalaxyhalos.Inparticular,itisnotcertainthatthedarkmatterdistributioncanmaintainaformthatresultsinapproximately atrotationcurvesforobjectsorbitinggalaxies.Recentsimulationsofstructureformation[6]arenotdetailedenoughatthescalesofinterestinordertoresolvethisquestion.

Weconsideraninteractionbetweenthescalar eldandthedarkmatterparticlesthatcanbemodelledthrougha eld-dependentparticlemass.Theactiontakestheform

S=

wheredτi= √dx4

2g µφ νφ U(φ) µν im(φ(xi))dτi+Sb,(1)

√ ggµν νφ= dU

dφTµµ,(2)

wheretheenergy-momentumtensorassociatedwiththegasofparticlesis

Tµν= dxµ1 idτim(φ(xi))δ(4)(x xi). gidτi(3)

Weareinterestedinstaticsphericallysymmetriccon gurations,withthescalar eldvaryingslowlywiththeradialdistancer.Ourtreatmentisrelevantuptoadistancer1～100kpcbeyondwhichthedarkmatterbecomesverydilute.Forr>～r1weexpectthatφquicklybecomesconstantwithavalueclosetoφ(r1)≡φ1.Thisisthevaluethatdrivesthepresentcosmologicalexpansion.Hereweassumethatthecosmologicalevolutionofφ1isnegligibleforthetimescalesofinterest,sothattheasymptoticcon gurationisstatictoagoodapproximation.

Weapproximate:m(φ) m(φ0)+[dm(φ0)/dφ]δφ≡m0+m′0δφ,withφ0thevalueofthe eldatthecenterofthegalaxy(r=0).Weworkwithintheleadingorderinδφandassumethatm′/m m′0/m0forallr.AlsodU/dφcanbeapproximatedbyaconstantbetweenr=0andr=∞.Forthescalar eldtoprovidearesolutionofthecoincidenceproblem,thetwotermsinther.h.s.ofeq.(2)mustbeofsimilarmagnitudeinthecosmologicalsolution.This

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We consider the possibility that the dark matter is coupled through its mass to a scalar field associated with the dark energy of the Universe. In order for such a field to play a role at the present cosmological distances, it must be effectively massless

meansthatdU/dφmustbecomparableto(m′0/m0)ρ∞.Weexpectρ∞tobeafractionofthe

3criticaldensity,i.e.ρ∞～3keV/cm.Ontheotherhand,theenergydensityinthecentral

3regionofthestaticsolution(r<～100kpc)isthatofthegalaxyhalo(～0.4GeV/cmforour

neighborhoodoftheMilkyWay).ThismakesdU/dφnegligibleinther.h.s.ofeq.(2)forastaticcon guration.Thepotentialisexpectedtobecomeimportantonlyforr→∞,wherethestaticsolutionmustbereplacedbythecosmologicalone.SimilarargumentsindicatethatwecanneglectUrelativetoρ.Alsothescalar eldmustbee ectivelymasslessatthegalacticscale.Forthesereasonsweexpectthattheformofthepotentialplaysanegligibleroleatthegalacticlevel.OuranalysiscanbecarriedoutwithU=0andismodelindependent.

Wetreatthedarkmatterasaweaklyinteracting,dilutegas.Wearemotivatedbythephenomenologicalsuccessoftheisothermalsphere[7]indescribingthe atpartoftherotationcurves.Wedonotaddressthequestionofthedensitypro leintheinnerpartofthegalaxies

µ(r<～5kpc).Weapproximatetheenergy-momentumtensorofthedarkmatterasTν=

2 =m(φ(r))n(r) v2 .Thedispersionofthedarkmatterdiag( ρ,p,p,p)withp(r)=ρ(r) vdd2velocityisassumedtobeconstantandsmall: vd 1.Thegravitational eldisconsideredintheNewtonianapproximation:g00 1+2Φ,withΦ=O(m′0δφ/m0).Intheweak eldlimit

andforp ρ,theconservationoftheenergy-momentumtensorgives

p= ρΦ ρ′′m′0

rΦ′=1

4M2

(δφ)=′ρBf rm′0

r

dz2+2

dz+expu+R

zc =0,(7)

whereu= αΦ α δφ,z=βr,zc=βrc,R=ρB/ρ0,andβ2=(1+κ2)αρ0/4M2.Theparameter2κ …… 此处隐藏：9445字，全部文档内容请下载后查看。喜欢就下载吧 ……