ASTROPHYSICS AND COSMOLOGY - CERN

1 ASTROPHYSICSANDCOSMOLOGYJ. Garc a-BellidoTheoreticalPhysicsGroup,Blacket tLaboratory, ImperialCollegeofScience,TechnologyandMe dicine,PrinceConsortRoad,LondonSW72BZ, therecentdevelopmentsin willdescribethestandardBigBangtheoryofth eevolutionoftheuniverse,withitssuccesses andshortcomings,whichwillleadto willpresenta reviewoftheveryrichphenomenologythatweha veincosmologytoday, aswellasevidencefortheobservationalrevol utionthatthisfieldis goingthrough,whichwillprovideus,inthenex tfewyears, (fromtheGreek:kosmos, universe,world,order, andlogos, word,theory)is probablythemostancientbodyofknowledge, ,untilrecently, wecouldonlyanswerto ,thanksto(whatelse?)rawdata,comingfrompr ecisemeasurementsofa ,weareenteringa precisioneraincosmology, andsoonmostofourobservableswillbemeasure dwitha fewpercentaccuracy.

2 We aretrulylivingintheGoldenAgeofCosmology. It is a veryexcitingtimeandI largesetofexperiments,whichpro-videcruci alinformationabouttheuniverseoriginandev olution;sorapidlythatthesenoteswillproba -blybeoutdatedbeforetheyareinprintasa ,someoftheresultsI mentioneddur-ingtheSummerSchoolhavealrea dybeenimproved, ,mostofthenewdatacanbeinterpretedwithina coherentframeworkknownasthestandardcosmo logicalmodel,basedontheBigBangtheoryofth euniverseandtheinflationaryparadigm,whic his willtryto makesucha theoreticalmodelaccesibleto youngexperimentalparticlephysicistswithl ittleornopreviousknowledgeaboutgeneralre lativityandcurvedspace-time, baseduponthesuccessfulhotBigBangtheory, whichex-plainsitsevolutionfromthefirstfr actionofa secondtoourpresentage, ,a theoreticalframeworkbasedongeneralrelati vity, asputfor-wardbyAlbertEinstein[1] [2] in the1920s,andthreerobustobservationalfact s.

3 First,theexpansionoftheuniverse,discover edbyEdwinP. Hubble[3] inthe1930s,asa reces-sionofgalaxiesat a ,therelativeabundanceoflightelements,exp lainedbyGeorgeGamow[4] inthe1940s,mainlythatofhelium,deuteriuma ndlithium,whichwerecookedfromthenuclearr eactionsthattookplaceat arounda secondtoa fewminutesaftertheBigBang,whentheunivers ewasa ,thecosmicmi-crowavebackground(CMB),thea fterglowoftheBigBang, RobertW. Wilson[5] asa veryisotropicblackbodyradiationat a temperatureofabout3 degreesKelvin,emittedwhentheuniversewasc oldenoughtoformneutralatoms,andphotonsde coupledfrommatter,approximately500, , theseobservationsareconfirmedto withina fewpercentaccuracy, Robertson WalkeruniversesWherearewein theuniverse?Duringourlectures,ofcourse,w ewerein CastaPapierni cka,in theheartofEurope ,onplanetEarth,rotating(8light-minutesaw ay)aroundtheSun, , theMilkyWay, whichis partofthelocalgroup,withintheVirgocluste rofgalaxies(ofsizea fewMpc),itselfpartofa supercluster(ofsize Mpc),withinthevisibleuniverse( Mpc),mostprobablya tinyhomogeneouspatchoftheinfiniteglobals tructureofspace-time, , , cosmologywasbornasasciencewiththeadvento fgeneralrelativityandtherealizationthatt hegeometryofspace-time,andthusthegeneral attractionofmatter, is determinedbytheenergycontentoftheunivers e[6], "!

4 # %$& ')( +*(1)Thesenon-linearequationsaresimplyto odifficulttosolvewithoutsomeinsightcomin gfromthesym-metriesoftheproblemat (1917-1922)theknown(observed)uni-verseex tendeda fewhundredsofparsecsaway, tothegalaxiesinthelocalgroup, ,bothEin-steinandFriedmannspeculatedthat themost reasonable symmetryfortheuniverseat largeshouldbehomogeneityatallpoints,andt husisotropy. It wasnotuntilthedetection,a fewdecadeslater, ,whatis themostgeneralmetricsatisfyinghomogeneit yandisotropyatlargescales?TheFriedmann-R obertson-Walker(FRW)metric,writtenherein termsoftheinvariantgeodesicdistance, -/. ,10 ,10 infourdimensions,2 3 3 314, seeRef.[6],2,5-. ,16. 87. 96;:,1<. 8=<.'<. 9, >.')? whichdeterminesthephysicalsizeoftheunive rse,anda constant=, whichcharacterizesthespatialcurvatureoft heuniverse,D E F G= ;:*=H IKJ#LNM=H OQPSRUT=H ' VWPXIKYZL#[(3)Spatiallyopen, , andthuscouldinprinciplebedistinguishedob servationally, ,wecanalsocomputea four-dimensionalspace-timecurvature,D \]F G^77'G_77.

5 'G=7.*(4)Dependingonthedynamics(andthuso nthematter/energycontent)oftheuniverse, , recollapsein (1pc),parsecforshort,correspondstoa `+acbed amusingiBjkbeverywhere, ,EdwinP. Hubbleobserveda redshiftinthespectraofdistantgalaxies,wh ichindicatedthattheywererecedingfromusat a velocityproportionalto theirdistanceto us[3]. Thiswascorrectlyinterpretedasmainlydueto theexpansionoftheuniverse,thatis,tothefa ctthatthescalefactortodayis , considerthemetricofaspatiallyflatunivers e,, -. , 6. :S,Ql0.(thegeneralizationofthefollowinga rgumenttocurvedspaceis straightforward).Thescalefactor796 :givesphysicalsizetothespatialcoordinate sl0, andtheexpansionis nothingbuta changeofscale(ofspatialunits) , thelocalattractionofmatter, galaxiesdonotmovein coordinatespace,it is thespace-timefabricwhichis ,theobservedwavelengthofphotonscomingfro mdistantobjectsis greaterthanwhentheywereemittedbya factorpreciselyequaltotheratioofscalefac tors,m npo;qm res 7 t7 '8u3(5)where7tis thepresentvalueofthescalefactor.

6 Sincetheuniversetodayis largerthaninthepast,theobservedwavelengt hswillbeshiftedtowardsthered,orredshifte d, byanamountcharacterizedbyu, FRWmetric,theuniverseexpansionis characterizedbya quantityknownastheHubblerateofexpansion, v96 : _796;:xw796 :, whosevaluetodayis denotedbyvt. AsI shalldeducelater,it is possibletocomputetherelationbetweentheph ysicaldistance, yandthepresentrateofexpansion,intermsoft heredshiftparameter,3vt, y u ' 9 {zt:u.'8|9uE:*(6)Atsmalldistancesfromus, ~} , wecansafelykeeponlythelinearterm,andthus therecessionvelocitybecomesproportionalt othedistancefromus, u vt, y, theproportionalityconstantbeingtheHubble rate,vt. Thisexpressionconstitutestheso-calledHub blelaw, andis spectacularlyconfirmedbya hugerangeofdata, ,onlyrecentlymeasurementsfromverybrighta nddistantsupernovae,atu , wereobtained,andarebeginningtoprobethese cond-orderterm,proportionaltothedecelera tionparameterz t, seeEq.

7 (22).I ,if allspatialdistancesarescaledwitha universalscalefactor, ourlocalmeasuringunits(ourrulers)shoulda lsobestretched,andthereforeweshouldnotse ethedifferencewhencomparingthetwodistanc es( )at becauseweliveina gravitationallyboundsystem, Inthisconsistentworldpicture,galaxiesare likepointparticles,movingasa a perfectfluid,onein whichanobservercomovingwiththefluidwould seetheuniversearoundit fluidcanbewrittenas[6]$ '9 ') :S 3(7)3 Thesubscript referstoLuminosity, (61).4 Thelocalspace-timeofa gravitationallyboundsystemis describedbytheSchwarzschildmetric,whichi s static[6].111 where 96;:and 96;:arethepressureandenergydensityofthef luidat a giventimeintheexpansion,and is thecomovingfour-velocity, satisfying .Letusnowwritetheequationsofmotionofsuch a , theseequationscanbededucedfromtheEinstei nequations(1),wherewesubstitutetheFRWmet ric(2)andtheperfectfluidtensor(7).

8 The2 componentoftheEinsteinequationsconstitut estheso-calledFriedmannequationv. _77. ;!# 4 '(4 = (8)whereI havetreatedthecosmologicalconstant(asa differentcomponentfrommatter. Infact,it canbeassociatedwiththevacuumenergyofquan tumfieldtheory, althoughwestilldonotunderstandwhyshouldi t havesucha smallvalue(120ordersofmagnitudebelowthat predictedbyquantumtheory),if itis , ($ ), a directconsequenceofthegeneralcovarianceo fthetheory( ), canbewrittenintermsoftheFRWmetricandthep erfectfluidtensor(7)as,,16 c7E') ,,167E B3(9)wheretheenergydensityandpressurecan besplitintoitsmatterandradiationcomponen ts, k' 3 5 ' 5 , withcorrespondingequationsofstate, 5 H 3 w4. Together, theFriedmannandtheenergy-conservationequ ationgivetheevolutionequationforthescale factor,^77 !)

9 # 49 '4 :'(43(10)I willnowmakea canwritetheHubbleparametertodayvtinunits of100kms Mpc & , intermsofwhichonecanestimatetheorderofma gnitudeforthepresentsizeandageoftheunive rse,vt B 8 & ? & " Q 1 & 3(11) v t 4 B & B Q 3(12)v t * 4Q & # *(13)Theparameter hasbeenmeasuredtobeintherange * fordecades,andonlyinthelastfewyearshasit beenfoundtoliewithin10%of *G . I , thatwhichin theabsenceofa cosmologicalconstantwouldcorrespondtoa flatuniverse, "!N * ..p # w E(14) * & p # w9 & :E3(15)where * EpEg is a correspondsto approximately4protonspercubicmeter, certainlya verydilutefluid!Intermsofthecriticaldens ityit is possibleto definetheratios B w , formatter, radiation,cosmologicalconstantandevencur vature,today, ;!)

10 # % "!# % (16) Q ( B = *(17)112 We canevaluatetodaytheradiationcomponent , correspondingto relativisticparticles,fromthedensityofmi crowavebackgroundphotons, & 9x $B :\w9p :E * Ep\ w E, whichgives * .. ,wecansafelyneglectthecontributionofrela tivisticparticlestothetotaldensityoftheu niversetoday,whichis dominatedeitherbynon-relativisticparticl es(baryons,darkmatterormassiveneutrinos) orbya cosmologicalconstant,andwritetherateofex pansionv .intermsofitsvaluetoday, : 7\t7\' 7Et7E' ' B *(18)Aninterestingconsequenceoftheserede finitionsis thatI cannowwritetheFriedmannequationtoday,7 7 t, asacosmicsumrule, ' Q ' B 3(19)wherewehaveneglected today. Thatis,in thecontextofa FRWuniverse,thetotalfractionofmatterdens ity, cosmologicalconstantandspatialcurvaturet odaymustaddupto ,if wemeasureoneofthethreecomponents,saythes patialcurvature, , wecanwritethematterandcosmologicalconsta ntasa functionofthescalefactor(7 tK ) 97: ;!)