宇宙学第四章当温度降至T0 3eV1eV104K原子大量产生从

)1endec/1+1en(1+zdec)/1-1=en/,=1+光子在退耦时满足nckT= Thisfull-skymapfromthe nckmissionshowsmatterbetweenEarthandtheedgeoftheobservableuniverse.Regionswithlessmassshowupaslighterareaswhileregionswithmoremassaredarker.Thegrayed-outareasarewherelightfromourowngalaxywastoobright,blockingnck'sabilitytomapthemoredistant1978年NobelPenziasand"fortheirdiscoveryofcosmic2006NobelJ.MatherandG."fortheirdiscoveryoftheblackbodyformandanisotropyofthecosmicmicrowavebackgroundl=0.29cmK~0.1TIn1948Alpherl=0.29cmK~0.1TIn1964Peeblesobtainedtheblackbodytemperatureof10K.Dicke,Peebles,Roll,andWilkinson searchingfortherelicradiation.In1964ArnoPenziasandRobertWilsondetectedhomogeneous3.5Kblackbodyradiationatthewavelengthof7.35cm.ThiswasprovedtobetheafterglowoftheBigBang,i.e.CMBR. CMBR 偶极不对称性(dipole由本星系群（~620km/s） (1–V DT=3.353对称和系尘埃辐射的影TheTheWilkinsonMicrowaveAnisotropyProbeLaunchedonJune30,2001,power-offOctCanmeasurefluctuationsinCMBonascaleof0.2o-TheFirstDetailedFullSkyPictureoftheOldestLightintheUniversenckLaunchedonMay,2001,power-offOctNinewavebandsrangingfrom30to857Themissionhadawidevarietyofscientificaims,1、highresolutiondetectionsofboththetotalintensityandpolarizationofprimordialCMBanisotropy2、creationofacatalogueofgalaxyclustersthroughtheSunyaev–Zel'dovich3、observationsofthegravitationallensingoftheCMB,aswellastheintegratedSachs–Wolfeeffect,4、observationsofbrightextragalacticradio(activegalacticnuclei)andinfrareddustygalaxy)sources,5、observationsoftheMilkyWay,includingtheinterslarmedium,distributedsynchrotronemissionandmeasurementsoftheGalacticmagneticfield,andstudiesoftheSolarSystem,includingnets,asteroids,cometsandthezodiacallight. DTDT=3.346mK DT/T~10---〉Doppler效应设在CMB背景辐射的参考系里光子的频率'nn0= ,n'(1-vcosq')n'0= (1-vcosq'TTobs= T(1-v2)1/1-vTTobs»T0(1+vcosq'+DDT=3.353–0.024mK(l,b)=(264o26–0o33,48o22–••••DDT=3.346–0.017mK••••lgalacticlongitudeb:galactic

DT/T~10-

:seedsoflarge-scale nckYY00q,f)=21pY01q,f)=2p3Y02q,f)=4plDT(q,j)lDT(q,j) lm aYl=2m=-

ClCl= 2l+1m=-ma lma*=<|lm|2C(qC(q)=DT(i1)DT(i2这里i1i2CC(q)=1(2l+1)CP P:Legendrepolynomialoforderll知道了Cl,就知道了它的所有的统计性质multipolesoftheCMBOtherballoonborneexperiments South 10 150and220GHzin95,150and220GHzinama 3frequencies(148,218,and2776 nck-thethirdgenerationCMBexperiment,launchedon14May2009,5full-skysurveysncknextgenerationCMBESA:COrE(Cosmicfullskytime-orderedthetemperatureanisotropiescanbeexpandedinspherical

a=

forGaussianrandomfluctuations,thestatisticalpropertiesofthetemperaturefieldaredeterminedbytheangularpowerspectrum =C =Cd Forafullsky,noiselessC2lC2cosmologicalparameterestimationlikelihoodfunctionforafullsky:thesky-cut,

T= ll

firstCMBd=-DT» Gd=-

DT=- 2 2=- 3 3总的效应：DT1

1Gd=-d 3 c2rsecondaryCMBanisotropies(after①thermalSunyaev-Zel’dovich②lensing③integratedSachs-WolffeaturesoflargeangularscalesintegratedSZeffect(<10)Silkdam :thedissipationofsmall-scaleperturbationscausedbyphotons'randomwalkingoutofoverdenseregions.Forfullaccuracy,theBoltzmannequationmustbesolvedtofollowtheevolutionofthephotondistributionfunction. atverysmall接近退耦时有限的光深JosephSilk ：：

overdenseregioncoldspoton质子之间通过Coulomb力耦合在一起 pressureimbalanceinphoton—baryonfluid wavestravelatspeed~c/√3beforebinationand~0thereaftercomovingsoundhorizon(RS~150Mpc) excesscorrelationofdensityfluctuationsat150Mpc excesscorrelationofgalaxiesat150Mpc.ThesoundspeedSoundspeedintheearlyUniversedependsonbaryons(matter)andradiation,so R=3ρb/ρrisproportionaltotheratiooftheenergydensityinnon-relativisticmattertothatinrelativisticmatter.pureIfradiationcontributesverylittletotheenergyThecomovingsizeofthesoundcrossinghorizonatbinationisthedistancesoundcouldtravelfromt=0tobination:Inmostmodels,theUniversewasmatterdominatedformanyexpansionstimespriortobination,(earlierstageswereradiationdominatedbutdidnotlastaslong)sowecanapproxima yassumethatonlythemattertermintheFriedmannequationisneededhere:priortobinationthebaryon-photonfluidoscillatesonsubhorizonscales.whythefluidoscillates(i.e.haswavespropagatingthroughit)insteadofcollapsingundergravity?Considersomefluidinagravitationalpotentialwell.Thebaryons,beingheavyandnonrelativistic,willtrytodragthefluidtothebottomofthewell,whiletheradiation,withphotonsbeingrelativistic,willwanttodisperseanyconcentrations.Thedynamicsofthissituationcanbediscussedwiththehelpoftworelevantphysicaleffects,gravityandfluidpressure,andthecorrespondingtime-scales.(Themoreaccurate First,gravity.Forsimplicity,imagineauniformdensitysphere.Atestparticlestartingfromrestatthesurfaceofasphereofuniformdensitywillacceleratetowardsthecenter,gotheothersideofthesphere,momentarilystop,andreversedirectionofmotion.Thewholeperiodofthatjourney,fromthestartingpoint,andbacktothestartingpointist0.Iftheparticleweretoorbitthesphere,theperiodoftheorbitwillalsobet0.Sot0isacharacteristictimescaleforauniformdensitysphere.Aquarteroft0iscalledthedynamicaltime,thetimeitwouldtakethetestparticletoreachthecenterofthesphere.FromNewtonianmechanicsdynamicaltimecanbeevaluatedtobe-fallNext,fluidpressure.Pressurewavespropagateatthesoundspeed.SoundcrossingtimeisλisthesizeoftheIfthedynamicaltimeismuchshorterthansoundcrossingtimethentheperturbation(i.e.densityenhancement)willsuccumbtogravityandcollapseintoaboundobject,inatimecomparabletotdyn.Ifsoundcrossingtimeismuchshorterthanthedynamicaltime,thenpressurewaveswillpropagateinthefluid,andwouldtrytodissipatetheperturbation.Thedividinglinebetweenthetwotypesofbehaviorcanbeexpressedintermsofascalelength,calledthe nslength(andthecorresponding nsmass).InourapproximatetreatmenttheHubbleexpansiontermcanbeneglected.UsingperturbedPoissonequation功率谱的峰的位置相应的波数为 1

rs(z*)

a2H 1+(3W/4Wa1a11+,H(a)=0Wa-3+Wa-2+WMkLMpc AngularsizeofthesoundhorizonatbinationTheangularsizeofsoundhorizonasseenbyusisthelocationofthefirstacousticpeakissensitivetothecurvatureoftheUniverse.Theangularsizeofthesoundhorizonatbinationdependsonthecurvatureoftheuniverse.Thesolidredarrowineachdiagramshowsthesoundhorizonatthetimeofbination.Thepathlightrayswilltakefromeithersideofthesoundhorizonwillbenddependingonthecurvatureoftheuniverse.Inaflatuniverse,theanglesofthetrianglesumto180degrees,andtheanglesubtendedisgivenbyEuclideangeometry.Inanopenuniverse,theanglesofthetrianglesumtolessthan180degrees,andtheanglethesoundhorizonsubtendsissmallerthantheK=0case.IfK>0,theanglesaddtomorethan180degrees,andtheangleislargerthanintheflatcaseCosmologyThetemp