Cosmological Crossroads : An Advanced Course in Mathematical

Thisbookisaneditedversionofthelecturesdeliveredduringthe1stAegean SummerSchoolonCosmology, heldonSamosisland, Greece, inSeptember 21-29,2001, andorganizedjointlybytheDepartmentofMathematics, U- versity of the Aegean and the Department of Physics, National Technical UniversityofAthens. Cosmology, thescienceoftheuniverse, standsatthecrossroadsofmany ?eldsofphysicsandmathematicsandpresentsuswithchallengingproblems of many forms. Although there are by now many textbooks discussing the subjectatmanylevels, itistruethatnosinglebookhasthecharacteristics wehadinmindwheneditingthisvolume. Wehavetriednottoproducea proceedingsvolumebutmoreamultiauthoredtextbookwhichcouldserveas areferencesourceofcurrentideasincosmology. Webelievethisbookcovers atanintroductorylevelmostoftheissueswhichareconsideredimportant inmoderncosmologicalresearchandcanbereadbyagraduatestudentor researcherwhowishestoacquireareasonableknowledgeofcosmologythat will, wehope, continuetobeofvalueforyearstocome. The 1st Aegean School on Cosmology, and consequently this book, - camepossiblewiththekindsupportofmanypeopleandorganizations. We received ?nancial support from the following sources and this is gratefully acknowledged: the Municipality of Karlovassi, the North Aegean Regional Secretariat, the Prefecture of Samos, the Ministry of the Aegean, and the NationalBankofGreece. TheadministrativesupportoftheSchoolwastakenupwithgreatcare byMrs. EvelynPappaandMantoKatsianiandwewouldliketothankthem bothfortheirkinde?ortstoresolvemanyissueswhicharosebefore, during andaftertheSchool. WeacknowledgethehelpofMr. NectariosBenekoswho designedandmaintainedthewebsiteoftheSchool. Last, butnotleast, wearegratefultothesta?ofSpringer-Verlag, resp- siblefortheLectureNotesinPhysics, whoseabilitiesandhelpcontributed greatlytothe?neappearanceofthisbook. Karlovassi, Samos, SpirosCotsakis March2002 EleftheriosPapantonopoulos TableofContents PartI HistoryandOverview 1 IsNatureGeneric? SpirosCotsakis, PeterG. L. Leach. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1. 2 PrinciplesofCosmologicalModelling. . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 2. 1 Spacetimes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1. 2. 2 TheoriesofGravity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 1. 2. 3 MatterFields. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 3 Cosmologies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1. 4 CosmologicalProblems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1. 4. 1 TheSingularityProblem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 1. 4. 2 TheProblemofCosmicTopology. . . . . . . . . . . . . . . . . . . . . 9 1. 4. 3 TheProblemofAsymptoticStates. . . . . . . . . . . . . . . . . . . . 9 1. 4. 4 GravityTheoriesandtheEarlyUniverse. . . . . . . . . . . . . . . 11 1. 5Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2 EvolutionofIdeasinModernCosmology AndreasParaskevopoulos. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2. 2