宇宙学chapter暗能量电磁相互作用微弱且基本是均匀分布因此主要研

Chapter5:Dark究它对宇宙膨胀的影响。暗能量的发现就是利用超观测不同超 Ia Riessetal. Perlmutteretal.High-ZSNSearch Riessetal. Perlmutteretal.Citation7713 Citation7840ExpansionAccelerating®DarkFriedmannHH2=a=3Gr+r+r+rkrmLFriedmann

Scale H2a

=3Gk+rr+rm+rL

Friedmann

Scale H2a

=3Gk+rr+rm+rL

W”

2Friedmann H2a

=3Gk+rr+rm+rLrp+aP3Friedmann H2a

=3Gk+rr+rm+rLrp+aP3=-4pGr+3p+

anon-zerocosmologicalconstantan tiontoGeneral=-4pGr+3p+

anon-zerocosmologicalconstantan tiontoGeneral=-4pGr+3p+

anon-zerocosmologicalconstantan tiontoGeneral=-4pGr+3p+

anon-zerocosmologicalconstant tiontoGeneralCosmicAcceleratingmatterisrequiredtofitcurrentAmountofw=-1Amountofw=-1matter(“DarkAmountof“ordinary”gravitating (IncludesDarkCosmicAcceleratingmatterisrequiredtofitcurrent

Preferredbydata2003Amountofw=-1matter(“DarkAmountofw=-1matter(“Dark (IncludesDarkCosmicAcceleratingmatterisrequiredtofitcurrent

Preferredbydata2008Amountofw=-1matter(“DarkAmountofw=-1matter(“Dark (IncludesDarkCosmicAcceleratingmatterisrequiredtofitcurrentSuzuki,Suzuki,etal.,Ap.J..Preferredbydata2012Preferredbydata2012Amountofw=-1matter(“Dark

Amountof“ordinary”gravitating (IncludesDarkDarkEnergy:EquationofTheequationofstateismostimportantparameterofdarkwhichmaybeafunctionofredshift.Inthiscase,wx(z)varieswithtime(orredshift).Institutingwx(z)intoa=-4pG(r+3pa3iiiTheconservationofenergytoWerewriteFriedmannObservationalconstraintsonequationofSuzukietal.TheSupernovaCosmologyWang&DaiAddDecelerationThegeneralizeddecelerationparametercanbedefinedq(z)

=-a/H(z)=-a2= q(z)>0,deceleration;q(z)<0, j(z)=/H(z)aj(z)=H4a

JerkparametersnapparameterHubbleparametercanbeexpressedInstitutingthisequationintoForaflatUniverse,Ωk=0,ΩM+Ωx=1,andForcaseofcosmologicalconstant(i.e.wx=-0 =1(W0

-2WLReissetal. WReissetal.Wecangetthetransitionredshiftq(z)=0:fromthisredshifttheUniversefromdecelerationto =[(1+3wx)(WM-

- MIntheΛCDMmodelwithΩM=0.3,ΩΛ=0.7,thetransitionredshiftiszq=0=(2ΩΛ/ΩM)- OurThesubtleslowingdownandspeedingupoftheexpansion,ofdistanceswithtime:a(t),mapsoutcosmichistoryliketreeringsmapouttheEarth’sclimateDarkenergyThesimplestmodelfordarkenergyisacosmologicalconstant(Λ).Theobservedenergydensityisr=L

thevacuumenergydensityevaluatedbythesumofzero-pointenergiesofquantumfieldswithmassmisgivenbyr=

¥d

k2+m2=

k2+

4p2However,weexpectthatquantumfieldtheoryisvaliduptosomecut-offscale

» FortheextremecaseofGeneralRelativity,weexpectittobevalidtojustbelowthenckscale:mpl=1.22×1019GeV,sokmax=mplrvac»1074GeV

Cosmologicalconstantproblem!宇宙常数R-1R-12mnRs-Rmn-12mnR=-8pGTT =-gLPP'=P-存在L

L提供了正密度(Lc2/8pG)，负压强(–Lc4/8pG)AdvocatedbyEinsteintoconstructastaticuniverse,butdiscardedafterthediscoveryoftheRevivedbyHoyle,Bondi,&Goldtosolveanagecrisis,butlaterresolvedbyasmallerHubblePutforthtoex intheabundanceofquasarsatz~2,butnowknowntobeduetotheevolutionofquasarsthemselves.由于观测数据不能排除状态方程参数小于-1quintessenceQuintom由于观测数据显示状态方程可能穿过-

Huterer&CoorayFengetal.generalizedChaplyginSNeBAOHubbleGRB H(z)

2= =H02

Wm+WL+W =1 2W0m1+z)+WL+Wk1+ 2Observations

ddL= c1+z)sin W+W-0mL+Wmz+W1H0L0Hz;,Lm=510dLcc2m,W)=N2L2557SNeDarkEnergy 宇宙微波背景辐射（目前已接近完善 （经验规律，系统误差星系团（经验规律，系统误差重子声波振荡（物理规律弱引力透镜（物理规律宙的大尺度结构，分别是2度视场巡天(TwodegreeFieldGalaxyRedshiftSurvey，简称2dFGRS)和斯隆数字天空勘测计划(SloanDigitalSkySurvey，简称是重子声波振荡aoncoustic简称数。100h-1Mpc) Ωb/Ωm的比值非常接近，其中Ωb和Ωm分别为宇宙中的重子和总的物质的平均密度(Whiteetal.计算宇宙学参数Ωb和Ωm。用这个方法测量Ωb和Ωm，最早是由White&Frenk ••BASICIDEA:GalaxyclustersaresolargethattheirmattercontentshouldprovideafairsampleofmattercontentofUniverse.fgas=X-fgas=X-raygasmassfgal= fbaryonfbaryon=fgal+fgas=fgas(1+0.19h0.5Sinceclustersprovide~fairsampleofUniverseWWm=bWb= Chandraresultson37regular,relaxedfgas(r)largescatteratsmallradiusbut→approxima yuniversalvalueatr2500:withinwhichthemassdensityis2500ρcritFitconstantvalueatForΩbh2=0.0214±0.0020(Kirkmanetal.‘03),h=0.72±0.08b=0.83±0.09(Ekeetal.98;Allenetal.(0.83–0.09)(0.0437–0.0041)h70-

dmanetal.Wm

(0.1175–0.0015)(1+0.16h700.5

=0.26–哈勃参量的优势在于,它无需通过积分就可以直接与宇宙学参量建立联系:H(z)=-dz/dt/(1+z)=H0E(z),其中dz/dt是红移z对宇宙时间t的导数,E(z)是红移和宇宙学参量的函数.总之,与标准光度距离方法相比,微分 (1观测到的dz/dt更加敏感于暗能量及其状态方程(2相关的精确测量可以利用地面望远镜进行(3)大大降低利用星系光谱测

体在发射相应光子时对应的宇宙的差Δt.应用恒星演化理论(该领域的研究已很透彻),我们可以通过研究分析恒星光谱得到它们的,进而应用之以反映宇宙,这样我们的问题就可但是,在宇宙学的尺度下,一个一个地去观测恒星是不切实际的,因为我们只能得到恒星的 也就是星系的光谱.但星系中可能包含不同的恒星族,而不同星族的形成时期会显著不同,因此 21H(z)TwoTwoindependentdarkenergytestswithgalaxyGrowthofstructureexperiments:thegrowthofstructureintheUniverseis(typically)inhibitedbydarkenergy.Inparticular,thiseffectsthelargestobjects(whichformlast)andsothenumberdensity,spatialclusteringandevolutionofclustersareallstrongfunctionsofdarkenergy.Directdistancemeasurements:justlikesupernovae,X-raystudiesofgalaxyclustersallowustomeasuredistancesindependentofredshift. Thisallowsustomeasurecosmicaccelerationdirectly.DarkEnergywithWeakGravitationalMassconcentrationsintheUniversedeflectphotonsfromdistantsources. cementofbackgroundimagesisunobservable,buttheirdistortion(shear)ismeasurable.Extentofdistortiondependsuponsizeofmassconcentrationsandrelativedistances.Depthinformationfromredshifts.Obtaining108redshiftsfromopticalspectroscopyisinfeasible.“photometric”redshiftsinstead.LensingmethodprobesbothD(z)andDarkDarkEnergywithWeakGravitationalInweaklensing,shapesofgalaxiesaremeasured.Dominantnoisesourceisthe(random)intrinsicshapeofgalaxies.Large-Nstatisticsextractlensinginfluencefromintrinsicnoise.CosmicCosmicDistanceWhenwemeasuretheenergydensityofdarkenergy,weneed“distance”and“redshift”relation.JustaftertheJustaftertheBigBang -RayTypeIaTypeIaTully-FisherTully-FisherRelationCepheidVariableFLHRFL

z=

L≡4πdGRBGRBLUMINOSITY(photonenergywiththehighestflux{liketheTIMEOFJET(whenafterglowfadingspeeds

MINIMUMRISE

NUMBEROF

Tjet5150051500400100001345Time(Sec)14Time(Sec)0

GRBluminosityGRBluminosity

V-LL- Eg-tRT-L

+bV+logL=a+blog(1+z)-1/0.1sEiso-Ep-

log(tb

(Amatietal. (Liang&Zhang L=4πdL2

Eg=(1-cosqjetGRBsareGRBsareanprobeofthe12GRBsDaietal(2004)Still,thecorrelationissostrikingthatjust15gStill,thecorrelationissostrikingthatjust15g rayburstsalreadyrevealthemasscontentoftheuniverseanditsexpansionnearlyaswellastypeIasupernovaeandothertechniques,Ghirlandasays.Histeamconfidentlycallsg raybursts“newrulerstomeasuretheuniverse”inthe20SeptemberAstrophysicalJournalLetters.AteamfromNanjingUniversity ,ledbyZigaoDai,reachedasimilarconclusion.Liang-Zhangcorrelation:LiangE.W.&ZhangB.2005,ApJ,633,20GRBs+157transitionredshift

LatestGRBluminosity

116GRBsWang,Dai&Qi2011DecelerationparameterJerkparameterSnap用557个SNeIa用dl(y)得到z<1.4的50GRBmm=im/s)/2iis-2sm=)