Cosmological constraint on unparticle dark matter

In unparticle dark matter (unmatter) model, the equation of state of the unmatter is given by $p=\rho/(2d_U+1)$, where $d_U$ is the scaling factor. Unmatter of such equation of state has significant impacts on the expansion history of the Universe. We use

EPJmanuscriptNo.

(willbeinsertedbytheeditor)

Cosmologicalconstraintonunparticledarkmatter

arXiv:0803.3223v1 [astro-ph] 21 Mar 2008

YanGongandXueleiChen

NationalAstronomicalObservatories,ChineseAcademyofSciences,20ADatunRd,ChaoyangDistrict,Beijing100012,China

Received:March20th,2008

Abstract.Inunparticledarkmatter(unmatter)model,theequationofstateoftheunmatterisgivenbyp=ρ/(2dU+1),wheredUisthescalingfactor.Unmatterofsuchequationofstatehassigni cantimpactsontheexpansionhistoryoftheUniverse.WeusethetypeIasupernovae(SNIa)andtheshiftparameterofthecosmicmicrowavebackground(CMB)toputconstraintonsuchunmattermodels.We ndthatifonlytheSNIadataisused,theconstraintisweak,butwiththeCMBshiftparameterdataaddedstrongconstraintscanbeobtained.FortheΛUDMmodel,inwhichunmatteristhesoledarkmatter,we ndthatdU>30at95%C.L.,renderingitpracticallyindistinguishablefromcolddarkmatter.FortheΛCUDMmodel,inwhichunmatterco-existswithcolddarkmatter,wefoundthattheunmattercanatmostmakeupafewpercentofthetotalcosmicdensityifdU<10.

1Introduction

Ithasrecentlybeenproposedthatahiddenscale-invariantsectorofmattermayexistandisnamed“unparticle”foritsunusualbehavior.Inthisscenario,thereisascaleinvariantsectorwithanon-trivialinfrared xedpoint,calledtheBanks-Zaks(BZ) eldTheBZ eldinter-actswiththestandardmodel(SM) eldsviaexchangeofparticlesofmassMU:

LBZ=

OBZOSM

2p0θ(p0)θ(p2)(p2)dU 2.

(1)

(2π)4

Forathermaldistributionofunparticles,thedensityandpressueisgivenby[26]

pU=gsT

4

T

4π2T

4π2

(2)(3)

ρU=(2dU+1)gsT4

kMU

OSMOU,

whereC(dU)=B(3/2,dU)Γ(2dU+2)ζ(2dU+2),and

B,Γ,ζaretheBeta,GammaandZetafunctions.Theequationofstatefortheunmatteristherefore

wU=1/(2dU+1)

(4)

whereCUisthecoe cientfunctionandOUistheunpar-ticleoperatorswithmassdimensiondU.PhenomelogicalconstraintsonMU,ΛU,CU,dUhavebeenderivedfromanumberofparticlephysicsandastrophysicsanaly-sis.

Giventhattheunparticlesinteractsweaklywithstan-dardmodelparticles,itisnaturaltoconsiderunparticlematter,orunmatter,asacandiateofdarkmatter,espe-ciallyiftheunparticlecouldbestablizedbyadiscretesymmetryThankstotheunusualkinematicsofun-particles,thebehaviorofunmatterisdistinctlydi erentfromtheusualcolddarkmatter.

Thus,astheuniverseexpands,theenergydensityofun-matterevolvesasρU(z)=ρU0(1+z)3(1+wU).IfdU=1,thisisthesameasradiation,andfordU→∞itsbehaviorwouldbesimilartocolddarkmatter.Intheintermediatecase,itsevolutionwoulddi erfrombothradiationandcolddarkmatter.Wecanthenusecosmologicalobserva-tionstoconstrainthevalueofdU.

Weshallconsidertwomodels.Inbothcasesweas-sumetheUniverseis atwithacosmologicalconstant.Inthe rstcase,denotedbyΛUDM,theunmatterservesasthesoledarkmatter,andthesetofcosmologicalpa-rametersθis{ b0, U0,dU,h0}.Inthesecondcase,denotedbyΛCUDM,besidestheunmatterthereisalsoacolddarkmatter,andthecosmologicalparametersset

In unparticle dark matter (unmatter) model, the equation of state of the unmatter is given by $p=\rho/(2d_U+1)$, where $d_U$ is the scaling factor. Unmatter of such equation of state has significant impacts on the expansion history of the Universe. We use

2YanGong,XueleiChen:Cosmologicalconstraintonunparticledarkmatter

θis{ m0, U0,dU,h0}.WethenusetheMCMCcodedevelopedinRef.[27]tomaketheglobal ttingandcon-straint.

Weconsidertwoobservationalconstraints.The rstoneisluminositydistancemodulitotypeIasupernovae,andthesecondoneisthesocalledshiftparameter[28,29],whichisessentiallyameasureofthedistancetothelastscatteringsurfaceofthecosmicmicrowavebackground(CMB),asmeasuredbytheWMAPthreeyearobserva-tion[30].Bothareconstraintsontheglobalexpansionhis-toryoftheUniverse,thoughtheapplicationoftheshiftparameterhascertainlimitations.Onemayalsoconsiderincludingadditionalconstraints,e.g.thebaryonacousticoscillationpeakmeasuredbytheSDSSlargescalestruc-turesurvey[31].However,theevolutionoflargescalestructureintheunmattermodelsmaydi erfromtheconventionalcolddarkmattermodels,sowehavenotin-cludedBAOdatainouranalysis.

TheWMAP3datagivesR=1.70±0.03[29],thuswehave

R 1.70

χ2R=

2Methods

TheexpansionrateH(z)isgivenby

2

H2(z)=H0 (z;θ),

(5)

whereforΛUDM:

(z;θ)= b0(1+z)3+ Λ0+ r0(1+z)4

+ U0(1+z)3(1+wU)

with Λ0=1 b0 U0 r0;

andforΛUCDM:

(z;θ)= m0(1+z)3+ Λ0+ r0(1+z)4

+ U0(1+z)3(1+wU);

(7)

with Λ0=1 m0 U0 r0.

Theluminositydistancetoasupernovaisthengivenby z

cdz′

dL(z;θ)=(1+z)

(6)

2σi

,(10)

whereµobs(zi)andσiaretheobservedvalueandthecor-respondingerrorforeachsupernova.Weuseadatasetof

182high-qualitySNIa[27]selectedfromtheGold06[32],SNLS[33]andESSENCE[34]samples.

TheCMBshiftparameterR[28]denotesthepositionsoftheacousticpeaksintheangularpowerspectrumofCMB,andtakestheformas

R=

H(z′)/H0

(11)

In unparticle dark matter (unmatter) model, the equation of state of the unmatter is given by $p=\rho/(2d_U+1)$, where $d_U$ is the scaling factor. Unmatter of such equation of state has significant impacts on the expansion history of the Universe. We use

YanGong,XueleiChen:Cosmologicalconstraintonunparticledarkmatter

3

Fig.1.The1σ,2σ,3σcontoursofthe UanddUintheΛUDMmodelderivedfromSNIaobservations.

FortheΛUDMmodel,thelowestedgeofthe2σ(95%C.L.)contourisabout30.Thus,smallvaluesofdU,whichismoreinterestingfromaphysicsperspective,isexcludedathighcon dencelevels.AtlargedUtheunmatterissim-ilartocolddarkmatter,soagainitisnotsurprisingthatthecentervalue …… 此处隐藏：9010字，全部文档内容请下载后查看。喜欢就下载吧 ……