理解暗能量和暗物质之间的相互作用

31 9 2007 9

HIGH

ENERGY

PHYSICS

AND

NUCLEAR

PHYSICS

Vol.31,No.9

Sep.,2007

UnderstandingtheInteractionbetweenDarkEnergy

andDarkMatter*

WANGBin1)

(DepartmentofPhysics,FudanUniversity,Shanghai200433,China)

AbstractWehavestudiedtheinteractionbetweendarkenergyanddarkmatterfromthethermodynamicalconsideration.Assumingtheinteractionasstablefluctuationsaroundequilibriumandusingthelogarithmiccorrectiontoentropycausedbythefluctuation,wehavederivedthephysicalexpressionoftheinteraction.Wehavetestedtheviabilityofourscenarioontheinteactionbyconfrontingwithcosmologicalobservations.

Keywordsdarkenergy,darkmatter,interaction

Avarietyofcosmologicalobservationssuggestaconcordantcompellingresultthatouruniverseisun-dergoinganacceleratedexpansiondrivenbydarken-ergy(DE).Despitetherobustobservationalevi-dence,thetheoreticalnatureandtheoriginofdarkenergyarestillthesourceofmuchdebate.Darkenergyisamajorpuzzleofthemoderncosmologywhichwasattractedalotofeffortstounderstanditinthepastyears.TheleadinginterpretationofsuchaDEisacosmologicalconstantwithequationofstate(EOS)wD=−1.AlthoughthecosmologicalconstantisthesimplesttheoreticalsolutiontoDEandisen-tirelyconsistentwiththecurrentobservationalcon-straints,thewell-knowncosmologicalconstantprob-lemconcerningwhythevacuumenergyissomuchsmallerthanthevaluefromtheeffectivefieldtheoryremainsunsolved.Thereareotherconjecturesrelat-ingtheDEtoascalarfieldcalledQuintessencewithwD>−1,ortoanexoticfieldcalledPhantomwithwD

[3][2]

[1]

analysesmildlyfavortheevolutionoftheDEparam-eterwDfromwD>−1towD

[2]

andthephantomsufferseven

moretheoreticalproblems[4].Besidesthesemodels,recently,anewDEmodelstimulatedbytheholo-graphicprinciplehasbeenputforward

[5]

anditwas

[6]

foundconsistentwiththeobservationaldata.MostdiscussionsonDErelyontheassumptionthatitsevolutionisindependentofothermatterfields.Onemightarguethatgiventheunknownna-tureofbothDEanddarkmatter(DM),anentirelyindependentbehaviorofDEandDMisveryspe-cial.StudiesontheinteractionbetweenDEandDMhavebeencarriedoutin

[7—12]

.Ithasbeenshown

thatthecouplingbetweenthequintessencefieldandDMcanprovideamechanismtogenerateaccelera-tionandalleviatethecoincidenceproblem

[7,12]

.In-

vestigationsonthesuitablecouplingbetweenholo-graphicDEandDMhavepresentedatheoreticalex-planationontheobservationaltransitionoftheDEEOSfromwD>−1towD

9 875

ΩDH),where

ΩD=ρD/(3H2).Takingderivativewithrespecttothescalefactoronbothsidesoftheeventhorizonexpression,wehave

H

ΩD

2ΩD

x=lna.

UsingtheFriedmannequationΩD+Ωm=1and

ΩD10

(1)—(3),wecanobtaintheEOSwD=−

.

(3)

wheretheprimeisthederivativewithrespectto

876 (HEP&NP) 31

2

Ω+

(4)

D

Ω .D

WiththesepreparationswecanexaminehowmuchtheeventhorizonwillchangeoveroneHubbletime,

tR

˙EH

D

ΩD

2−

Ω

2

ln(CT2),whereCistheheatcapacity

[19]

.

Inourcase,theheatcapacityoftheDEcanbecal-culatedasC=

1∂T

=−(2πRE)2πc2(1+3w0)R2

DE,whichispositivesinceforDE1+3w0

D

readsS1=−

1

2ln

2πc

dS1

ΩD

c2πRE

万方数据

8πQ

H

ΩD+3(1+wD)ΩD=−

Ωm+3Ω8πQ

H

m=

ΩD

3H3Ω.(14)

D

ComparingwithEq.(9),wecanobtaintheinterac-

tiontermQintheform

−8πQ

dS1

πc2RE

dS1

3πc2RE

ΩD)andusingEq.(8),wehavedS1

ΩD/c−1)

HΩ D

ΩD−1

−

Ω.

DBesides,usingtheFriedmannequation−1)

(16)

and(3),

9 877

Ω+(ΩDD−1)+2√c

(ΩD−1)=−

8πQ

1√H2Ω2

Ω−

c

+

D

D

ΩD

ΩD

πc4

.(18)

WithEqs.(18)and(3)athand,weareinaposi-tiontodiscussthedependenceoftheevolutionofDEwithrespecttothecouplingtoDM.Inthenumericalcalculation,wesetc=1.FromFig.1welearnthatwiththeinteractionbetweenDEandDM,DEstartstobeeffectiveearlier.Withtheinteraction,DEandDMfolloweachother,asdisplayedinFig.2.WeseefromFig.2(a)and2(b)thatwiththeinteraction,ρm=ρDearlierthanthecasewithoutinteraction.Toobservemoreclearly,wecandefinetheratiobe-tweenenergydensitiesr=ρm/ρ[7]

D

andinvestigateits

changewiththescalefactor.ThebehaviorisshowninFig.2(c).risamonotonousdecreasingfunctionofthescalefactor,andaroundthepresenttimeitvariesveryslowly.Comparedwiththenoninteractingcase,wefindintherecenterathemonotonousdecreaseofrisslowerwhenthereisaninteractionbetweenDEandDM.ThismeansthatintherecenthistoryoftheuniverseDEisbeingtransformedintoDMduetotheircoupling.Thisresultgotbyemployingthederivedinteractionfromentropycorrectionisconsis-tentwiththeearlierresultinthephenomenologicalinteractionmodel

[10]

andinthestudyoftheinter-actingquintessencemodel[7]

.ThedifferentevolutionoftheDMduetoitsinteractionwithDEgivesrisetothedifferentexpansionhistoryoftheuniverseanddifferentevolutionofthematterdensityperturbationwhichmodifiesthestructureformation.InRef.[8,10]thematterdensityperturbationsintheinteractingmodelshavebeeninvestigatedandinRef.[10]theinfluencetotheDMdensityperturbationduetotheinteractionbetweenDEandDMhasbeenusedtoexplainwhyitispossible,asrecentlyobserved,foranoldquasartobeobservedintheearlystagesoftheuniverse.Asacomparison,inFig.1and2wehavealsoincludedtheresultbyconsideringthephe-

万方数据

nomenologicalinteractionbetweenDEandDMwith

constantcouplingb.ItiseasytoseethattheresultontheevolutionofDEandDMbyusingthephe-nomenologicalmodelisconsistentwiththeresultgot

byusingtheinteractionderivedfromthethermody-namicalconsideration.

Fig.1.EvolutionsofΩDandΩmwithandwithoutinteraction.Linesshowingvaluesin-creasingwithaareΩD,andthedecreasinglinesareforΩm.Thesolidlineistheresultofourmodel,thedottedlineistheresultwithoutinteractionandthedashedlineisforthesim-plephenomenologicalmodelwithb2=0.06.

Fig.2.EvolutionsofρDandρmwithandwith-outinteraction.Beforethecrossingpoint,linesontheleftareforρD,otherbunchesoflinesareforρm.Thesolidlineistheresultofourmodel,thedottedlineistheresultwithoutinteractionandthedashedlineisforthesim-plephenomenologicalmodelwithb2=0.06.

IncludingtheinteractionbetweenDEandDMwiththeformderivedfromentropycorrection,ourmodelnaturallyshowsthatouruniversehasanac-celeratedexpansioninthelatestageandontheotherhanditalsodisplaysadecelerationintheearlytime.InFig.3,weshowthedependenceofthedecelera-tionparameteronthecouplingbetweenDEandDM.Thisresultisalsosimilartothatgotbyusingthephenomenologicalinteraction[9]

.

WenowdiscusstheEOSofDEwiththeinterac-tionbetweenDEandDM.Wefoundthatwithourderivedinteractionform,theDEnaturallyhasatran-sitionasindicatedbyrecentobservationswithwDcrossingtheborder−1.Thisresultispresentedin

878 (HEP&NP) 31

dS1

3πc2RE

9 879

References

1RiessAGetal.Astron.J.,1998,116:1009;PerlmutterSetal.Astrophys.J.,1999,517:565;PerlmutterSetal.As-trophys.J.,2003,598:102;deBernardisPetal.Nature,2000,404:955

2PadmanabhanT.Phys.Rept.,2003,380:235.hep-th/0212290;PeeblesPJE,RatraB.Rev.Mod.Phys.,2003,75:559.astro-ph/0207347;SahniV.astro-ph/04033243AlamU,SahniV,StarobinskyAA.JCAP,2004,0406:008;HutererD,CoorayA.Phys.Rev.,2005,D71:023506;WANGY,TegmarkM.astro-ph/0501351;JassalHK,BaglaJS,PadmanabhanT.astro-ph/0506748

4CarrollSM,HoffmanM,TroddenM.Phys.Rev.,2003,D68:023509;ClineJM,JeonSY,MooreGD.Phys.Rev.,2004,D70:043543;HsuSDH,JenkinsA,WiseMB.Phys.Lett.,2004,B597:2705LIM.Phys.Lett.,2004,B603:1

6HUANGQG,GONGYG.JCAP,2004,0408:006;GONGYG,WANGB,ZHANGYZ.Phys.Rev.,2005,D72:043510;ZHANGX.astro-ph/0504586;SHENJY,WANGB,AbdallaEetal.Phys.Lett.,2005,B609:200;HUANGZY,WANGB,AbdallaEetal.JCAP,2006,0605:013;ElizaldeE,NojiriS,OdintsovSDetal.hep-th/0502082;WANGBin,GONGYun-Gui,SURu-Keng.Phys.Lett.,2005,B605:9—14;WANGBin,ElcioAb-dalla,SURu-Keng.Phys.Lett.,2005,B611:21—267SergiodelCampo,RamonHerrera,GermanOlivares,DiegoPavon.Phys.Rev.,2006,D74:023501;Sergiodelcampo,RamonHerrera,DiegoPavon.Phys.Rev.,2005,D71:123529;DiegoPavon,WinfriedZimdahl.Phys.Lett.,2005,B628:206—210;GermanOlivares,FernandoAtrio-Barandela,DiegoPavon.Phys.Rev.,2005,D71:0635238OlivaresG,Atrio-BarandelaF,PavonD.Phys.Rev.,2006,

D74:043521

9WANGBin,GONGYun-Gui,ElcioAbdalla.Phys.Lett.,2005,B624:141—146;WANGBin,LINChi-Yong,ElcioAbdalla.Phys.Lett.,2006,B637:357—361

10WANGBin,ZANGJia-Dong,LINChi-Yongetal.astro-ph/0607126

11SubinoyDas,PierStefanoCorasaniti,JustinKhoury.Phys.

Rev.,2006,D73:083509

12LucaAmendola,ShinjiTsujikawa,SamiM.Phys.Lett.,

2006,B632:155—158;LucaAmendola,ClaudiaQuer-cellini.Phys.Rev.,2003,D68:023514;AndersonGW,CarrollSM.arXiv:astro-ph/971128813BeanR.Phys.Rev.,2001,D64:12351614ZimdanlW.gr-qc/0505056

15PiazzaF,TsujikawaS.JCAP,2004,0407:00416NikodemJ.Poplawski.gr-qc/0608031

17GibbonsGW,HawkingSW.Phys.Rev.,1977,D15:273818RaphaelBousso.Phys.Rev.,2005,D71:064024

19SauryaDas,ParthasarathiMajumdar,RajatK.Bhaduri.

Class.Quant.Grav.,2002,19:2355—2368

20C´ecileBarbachoux,J´eromeGariel,G´erardLeDenmat.

astro-ph/0603299

21CohenA,KaplanD,NelsonA.Phys.Rev.Lett.,1999,82:

4971

22GermanIzquierdo,DiegoPavon.gr-qc/0606014;German

Izquierdo,DiegoPavon.Phys.Lett.,2006,B633:420—426

23FriacaA,AlcanizJS,LimaJAS.Mon.Not.Roy.Astron.

Soc.,2005,362:1295;HasingerG,SchartelN,KomossaS.Astrophys.J.,2002,573:L77;KomossaS,HasingerG.inXEUSstudyingtheevolutionoftheuniverse

24SpergelDNetal.astroph/0603449ApJ;SpergelDNet

al.Astrophys.J.,2003,148(Suppl.):175

*

(

1)

200433)

. , , .

31 9 2007 9

HIGH

ENERGY

PHYSICS

AND

NUCLEAR

PHYSICS

Vol.31,No.9

Sep.,2007

UnderstandingtheInteractionbetweenDarkEnergy

andDarkMatter*

WANGBin1)

(DepartmentofPhysics,FudanUniversity,Shanghai200433,China)

AbstractWehavestudiedtheinteractionbetweendarkenergyanddarkmatterfromthethermodynamicalconsideration.Assumingtheinteractionasstablefluctuationsaroundequilibriumandusingthelogarithmiccorrectiontoentropycausedbythefluctuation,wehavederivedthephysicalexpressionoftheinteraction.Wehavetestedtheviabilityofourscenarioontheinteactionbyconfrontingwithcosmologicalobservations.

Keywordsdarkenergy,darkmatter,interaction

Avarietyofcosmologicalobservationssuggestaconcordantcompellingresultthatouruniverseisun-dergoinganacceleratedexpansiondrivenbydarken-ergy(DE).Despitetherobustobservationalevi-dence,thetheoreticalnatureandtheoriginofdarkenergyarestillthesourceofmuchdebate.Darkenergyisamajorpuzzleofthemoderncosmologywhichwasattractedalotofeffortstounderstanditinthepastyears.TheleadinginterpretationofsuchaDEisacosmologicalconstantwithequationofstate(EOS)wD=−1.AlthoughthecosmologicalconstantisthesimplesttheoreticalsolutiontoDEandisen-tirelyconsistentwiththecurrentobservationalcon-straints,thewell-knowncosmologicalconstantprob-lemconcerningwhythevacuumenergyissomuchsmallerthanthevaluefromtheeffectivefieldtheoryremainsunsolved.Thereareotherconjecturesrelat-ingtheDEtoascalarfieldcalledQuintessencewithwD>−1,ortoanexoticfieldcalledPhantomwithwD

[3][2]

[1]

analysesmildlyfavortheevolutionoftheDEparam-eterwDfromwD>−1towD

[2]

andthephantomsufferseven

moretheoreticalproblems[4].Besidesthesemodels,recently,anewDEmodelstimulatedbytheholo-graphicprinciplehasbeenputforward

[5]

anditwas

[6]

foundconsistentwiththeobservationaldata.MostdiscussionsonDErelyontheassumptionthatitsevolutionisindependentofothermatterfields.Onemightarguethatgiventheunknownna-tureofbothDEanddarkmatter(DM),anentirelyindependentbehaviorofDEandDMisveryspe-cial.StudiesontheinteractionbetweenDEandDMhavebeencarriedoutin

[7—12]

.Ithasbeenshown

thatthecouplingbetweenthequintessencefieldandDMcanprovideamechanismtogenerateaccelera-tionandalleviatethecoincidenceproblem

[7,12]

.In-

vestigationsonthesuitablecouplingbetweenholo-graphicDEandDMhavepresentedatheoreticalex-planationontheobservationaltransitionoftheDEEOSfromwD>−1towD

9 875

ΩDH),where

ΩD=ρD/(3H2).Takingderivativewithrespecttothescalefactoronbothsidesoftheeventhorizonexpression,wehave

H

ΩD

2ΩD

x=lna.

UsingtheFriedmannequationΩD+Ωm=1and

ΩD10

(1)—(3),wecanobtaintheEOSwD=−

.

(3)

wheretheprimeisthederivativewithrespectto

876 (HEP&NP) 31

2

Ω+

(4)

D

Ω .D

WiththesepreparationswecanexaminehowmuchtheeventhorizonwillchangeoveroneHubbletime,

tR

˙EH

D

ΩD

2−

Ω

2

ln(CT2),whereCistheheatcapacity

[19]

.

Inourcase,theheatcapacityoftheDEcanbecal-culatedasC=

1∂T

=−(2πRE)2πc2(1+3w0)R2

DE,whichispositivesinceforDE1+3w0

D

readsS1=−

1

2ln

2πc

dS1

ΩD

c2πRE

万方数据

8πQ

H

ΩD+3(1+wD)ΩD=−

Ωm+3Ω8πQ

H

m=

ΩD

3H3Ω.(14)

D

ComparingwithEq.(9),wecanobtaintheinterac-

tiontermQintheform

−8πQ

dS1

πc2RE

dS1

3πc2RE

ΩD)andusingEq.(8),wehavedS1

ΩD/c−1)

HΩ D

ΩD−1

−

Ω.

DBesides,usingtheFriedmannequation−1)

(16)

and(3),

9 877

Ω+(ΩDD−1)+2√c

(ΩD−1)=−

8πQ

1√H2Ω2

Ω−

c

+

D

D

ΩD

ΩD

πc4

.(18)

WithEqs.(18)and(3)athand,weareinaposi-tiontodiscussthedependenceoftheevolutionofDEwithrespecttothecouplingtoDM.Inthenumericalcalculation,wesetc=1.FromFig.1welearnthatwiththeinteractionbetweenDEandDM,DEstartstobeeffectiveearlier.Withtheinteraction,DEandDMfolloweachother,asdisplayedinFig.2.WeseefromFig.2(a)and2(b)thatwiththeinteraction,ρm=ρDearlierthanthecasewithoutinteraction.Toobservemoreclearly,wecandefinetheratiobe-tweenenergydensitiesr=ρm/ρ[7]

D

andinvestigateits

changewiththescalefactor.ThebehaviorisshowninFig.2(c).risamonotonousdecreasingfunctionofthescalefactor,andaroundthepresenttimeitvariesveryslowly.Comparedwiththenoninteractingcase,wefindintherecenterathemonotonousdecreaseofrisslowerwhenthereisaninteractionbetweenDEandDM.ThismeansthatintherecenthistoryoftheuniverseDEisbeingtransformedintoDMduetotheircoupling.Thisresultgotbyemployingthederivedinteractionfromentropycorrectionisconsis-tentwiththeearlierresultinthephenomenologicalinteractionmodel

[10]

andinthestudyoftheinter-actingquintessencemodel[7]

.ThedifferentevolutionoftheDMduetoitsinteractionwithDEgivesrisetothedifferentexpansionhistoryoftheuniverseanddifferentevolutionofthematterdensityperturbationwhichmodifiesthestructureformation.InRef.[8,10]thematterdensityperturbationsintheinteractingmodelshavebeeninvestigatedandinRef.[10]theinfluencetotheDMdensityperturbationduetotheinteractionbetweenDEandDMhasbeenusedtoexplainwhyitispossible,asrecentlyobserved,foranoldquasartobeobservedintheearlystagesoftheuniverse.Asacomparison,inFig.1and2wehavealsoincludedtheresultbyconsideringthephe-

万方数据

nomenologicalinteractionbetweenDEandDMwith

constantcouplingb.ItiseasytoseethattheresultontheevolutionofDEandDMbyusingthephe-nomenologicalmodelisconsistentwiththeresultgot

byusingtheinteractionderivedfromthethermody-namicalconsideration.

Fig.1.EvolutionsofΩDandΩmwithandwithoutinteraction.Linesshowingvaluesin-creasingwithaareΩD,andthedecreasinglinesareforΩm.Thesolidlineistheresultofourmodel,thedottedlineistheresultwithoutinteractionandthedashedlineisforthesim-plephenomenologicalmodelwithb2=0.06.

Fig.2.EvolutionsofρDandρmwithandwith-outinteraction.Beforethecrossingpoint,linesontheleftareforρD,otherbunchesoflinesareforρm.Thesolidlineistheresultofourmodel,thedottedlineistheresultwithoutinteractionandthedashedlineisforthesim-plephenomenologicalmodelwithb2=0.06.

IncludingtheinteractionbetweenDEandDMwiththeformderivedfromentropycorrection,ourmodelnaturallyshowsthatouruniversehasanac-celeratedexpansioninthelatestageandontheotherhanditalsodisplaysadecelerationintheearlytime.InFig.3,weshowthedependenceofthedecelera-tionparameteronthecouplingbetweenDEandDM.Thisresultisalsosimilartothatgotbyusingthephenomenologicalinteraction[9]

.

WenowdiscusstheEOSofDEwiththeinterac-tionbetweenDEandDM.Wefoundthatwithourderivedinteractionform,theDEnaturallyhasatran-sitionasindicatedbyrecentobservationswithwDcrossingtheborder−1.Thisresultispresentedin

878 (HEP&NP) 31

dS1

3πc2RE

9 879

References

1RiessAGetal.Astron.J.,1998,116:1009;PerlmutterSetal.Astrophys.J.,1999,517:565;PerlmutterSetal.As-trophys.J.,2003,598:102;deBernardisPetal.Nature,2000,404:955

2PadmanabhanT.Phys.Rept.,2003,380:235.hep-th/0212290;PeeblesPJE,RatraB.Rev.Mod.Phys.,2003,75:559.astro-ph/0207347;SahniV.astro-ph/04033243AlamU,SahniV,StarobinskyAA.JCAP,2004,0406:008;HutererD,CoorayA.Phys.Rev.,2005,D71:023506;WANGY,TegmarkM.astro-ph/0501351;JassalHK,BaglaJS,PadmanabhanT.astro-ph/0506748

4CarrollSM,HoffmanM,TroddenM.Phys.Rev.,2003,D68:023509;ClineJM,JeonSY,MooreGD.Phys.Rev.,2004,D70:043543;HsuSDH,JenkinsA,WiseMB.Phys.Lett.,2004,B597:2705LIM.Phys.Lett.,2004,B603:1

6HUANGQG,GONGYG.JCAP,2004,0408:006;GONGYG,WANGB,ZHANGYZ.Phys.Rev.,2005,D72:043510;ZHANGX.astro-ph/0504586;SHENJY,WANGB,AbdallaEetal.Phys.Lett.,2005,B609:200;HUANGZY,WANGB,AbdallaEetal.JCAP,2006,0605:013;ElizaldeE,NojiriS,OdintsovSDetal.hep-th/0502082;WANGBin,GONGYun-Gui,SURu-Keng.Phys.Lett.,2005,B605:9—14;WANGBin,ElcioAb-dalla,SURu-Keng.Phys.Lett.,2005,B611:21—267SergiodelCampo,RamonHerrera,GermanOlivares,DiegoPavon.Phys.Rev.,2006,D74:023501;Sergiodelcampo,RamonHerrera,DiegoPavon.Phys.Rev.,2005,D71:123529;DiegoPavon,WinfriedZimdahl.Phys.Lett.,2005,B628:206—210;GermanOlivares,FernandoAtrio-Barandela,DiegoPavon.Phys.Rev.,2005,D71:0635238OlivaresG,Atrio-BarandelaF,PavonD.Phys.Rev.,2006,

D74:043521

9WANGBin,GONGYun-Gui,ElcioAbdalla.Phys.Lett.,2005,B624:141—146;WANGBin,LINChi-Yong,ElcioAbdalla.Phys.Lett.,2006,B637:357—361

10WANGBin,ZANGJia-Dong,LINChi-Yongetal.astro-ph/0607126

11SubinoyDas,PierStefanoCorasaniti,JustinKhoury.Phys.

Rev.,2006,D73:083509

12LucaAmendola,ShinjiTsujikawa,SamiM.Phys.Lett.,

2006,B632:155—158;LucaAmendola,ClaudiaQuer-cellini.Phys.Rev.,2003,D68:023514;AndersonGW,CarrollSM.arXiv:astro-ph/971128813BeanR.Phys.Rev.,2001,D64:12351614ZimdanlW.gr-qc/0505056

15PiazzaF,TsujikawaS.JCAP,2004,0407:00416NikodemJ.Poplawski.gr-qc/0608031

17GibbonsGW,HawkingSW.Phys.Rev.,1977,D15:273818RaphaelBousso.Phys.Rev.,2005,D71:064024

19SauryaDas,ParthasarathiMajumdar,RajatK.Bhaduri.

Class.Quant.Grav.,2002,19:2355—2368

20C´ecileBarbachoux,J´eromeGariel,G´erardLeDenmat.

astro-ph/0603299

21CohenA,KaplanD,NelsonA.Phys.Rev.Lett.,1999,82:

4971

22GermanIzquierdo,DiegoPavon.gr-qc/0606014;German

Izquierdo,DiegoPavon.Phys.Lett.,2006,B633:420—426

23FriacaA,AlcanizJS,LimaJAS.Mon.Not.Roy.Astron.

Soc.,2005,362:1295;HasingerG,SchartelN,KomossaS.Astrophys.J.,2002,573:L77;KomossaS,HasingerG.inXEUSstudyingtheevolutionoftheuniverse

24SpergelDNetal.astroph/0603449ApJ;SpergelDNet

al.Astrophys.J.,2003,148(Suppl.):175

*

(

1)

200433)

. , , .