TASI Lectures Introduction to Cosmology

arXiv:astro-ph/0401547v126Jan2004TASILectures:IntroductiontoCosmologyMarkTrodden1andSeanM.Carroll21DepartmentofPhysicsSyracuseUniversitySyracuse,NY13244-1130,USA2EnricoFermiInstitute,DepartmentofPhysics,andCenterforCosmologicalPhysicsUniversityofChicago5640S.EllisAvenue,Chicago,IL60637,USAFebruary2,2008AbstractTheseproceedingssummarizelecturesthatweredeliveredaspartofthe2002and2003TheoreticalAdvancedStudyInstitutesinelementaryparticlephysics(TASI)attheUniversityofColoradoatBoulder.Theyareintendedtoprovideapedagogicalintroductiontocosmologyaimedatadvancedgraduatestudentsinparticlephysicsandstringtheory.SU-GP-04/1-11Contents1Introduction42FundamentalsoftheStandardCosmology42.1HomogeneityandIsotropy:TheRobertson-WalkerMetric..........42.2Dynamics:TheFriedmannEquations......................82.3FlatUniverses...................................112.4IncludingCurvature...............................122.5Horizons......................................132.6Geometry,DestinyandDarkEnergy......................153OurUniverseTodayandDarkEnergy163.1Matter:OrdinaryandDark...........................163.2SupernovaeandtheAcceleratingUniverse...................193.3TheCosmicMicrowaveBackground.......................213.4TheCosmologicalConstantProblem(s).....................263.5DarkEnergy,orWorse?.............................304EarlyTimesintheStandardCosmology354.1DescribingMatter.................................354.2ParticlesinEquilibrium.............................364.3ThermalRelics..................................404.4Vacuumdisplacement...............................424.5PrimordialNucleosynthesis............................434.6FiniteTemperaturePhaseTransitions......................454.7TopologicalDefects................................474.8Baryogenesis....................................534.9BaryonNumberViolation............................544.9.1B-violationinGrandUnifiedTheories.................544.9.2B-violationintheElectroweaktheory..................554.9.3CPviolation................................564.9.4DeparturefromThermalEquilibrium..................574.9.5Baryogenesisvialeptogenesis......................584.9.6Affleck-DineBaryogenesis........................585Inflation595.1TheFlatnessProblem..............................595.2TheHorizonProblem...............................605.3UnwantedRelics.................................625.4TheGeneralIdeaofInflation..........................635.5Slowly-RollingScalarFields...........................635.6AttractorSolutionsinInflation.........................6525.7SolvingtheProblemsoftheStandardCosmology...............665.8VacuumFluctuationsandPerturbations....................675.9ReheatingandPreheating............................695.10TheBeginningsofInflation...........................7031IntroductionThelastdecadehasseenanexplosiveincreaseinboththevolumeandtheaccuracyofdataobtainedfromcosmologicalobservations.Thenumberoftechniquesavailabletoprobeandcross-checkthesedatahassimilarlyproliferatedinrecentyears.Theoreticalcosmologistshavenotbeenslouchesduringthistime,either.However,itisfairtosaythatwehavenotmadecomparableprogressinconnectingthewonderfulideaswehavetoexplaintheearlyuniversetoconcretefundamentalphysicsmodels.Oneofourhopesintheselecturesistoencouragethedialoguebetweencosmology,particlephysics,andstringtheorythatwillbeneededtodevelopsuchaconnection.Inthispaper,wehavecombinedmaterialfromtwosetsofTASIlectures(givenbySMCin2002andMTin2003).Wehavetakentheopportunitytoaddmoredetailthanwasoriginallypresented,aswellastoincludesometopicsthatwereoriginallyexcludedforreasonsoftime.Ourintentistoprovideaconciseintroductiontothebasicsofmoderncosmologyasgivenbythestandard“ΛCDM”Big-Bangmodel,aswellasanoverviewoftopicsofcurrentresearchinterest.InLecture1wepresentthefundamentalsofthestandardcosmology,introducingevidenceforhomogeneityandisotropyandtheFriedmann-Robertson-Walkermodelsthatthesemakepossible.InLecture2weconsidertheactualstateofourcurrentuniverse,whichleadsnaturallytoadiscussionofitsmostsurprisingandproblematicfeature:theexistenceofdarkenergy.InLecture3weconsidertheimplicationsofthecosmologicalsolutionsobtainedinLecture1forearlytimesintheuniverse.Inparticular,wediscussthermodynamicsintheexpandinguniverse,finite-temperaturephasetransitions,andbaryogenesis.Finally,Lecture4containsadiscussionoftheproblemsofthestandardcosmologyandanintroductiontoourbest-formulatedapproachtosolvingthem–theinflationaryuniverse.Ourreviewisnecessarilysuperficial,giventhelargenumberoftopicsrelevanttomoderncosmology.Moredetailcanbefoundinseveralexcellenttextbooks[1,2,3,4,5,6,7].Throughoutthelectureswehaveborrowedliberally(andsometimesverbatim)fromearlierreviewsofourown[8,9,10,11,12,13,14,15].Ourmetricsignatureis−+++.Weuseunitsinwhich¯h=c=1,anddefinethereducedPlanckmassbyMP≡(8πG)−1/2≃1018GeV.2FundamentalsoftheStandardCosmology2.1HomogeneityandIsotropy:TheRobertson-WalkerMetricCosmologyastheapplicationofgeneralrelativity(GR)totheentireuniversewouldseemahopelessendeavorwereitnotforaremarkablefact–theuniverseisspatiallyhom