Cosmological Crossroads: An Advanced Course in Mathematical, Physical and String Cosmology

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Spiros Cotsakis, Eleftherios Papantonopoulos
Springer Science & Business Media, Nov 7, 2002 - Science - 480 pages
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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 TheBeginningsofModernCosmology(1917-1950). . . . . . . . . . . . . 17 2. 3 Cosmology1950-1970:HotBigBang, SingularitiesandQuantumApproach. . . . . . . . . . . . . . . . . . . . . . . . . 20 2. 4 Cosmology1970-1990:Chaotic,In'ationary, QuantumandAlternative. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22 2. 5ConclusionsandOutlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 VIII TableofContents PartII MathematicalCosmology 3ConstraintsandEvolutioninCosmology YvonneChoquet-Bruhat,JamesW. York. . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3. 1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3. 2 MovingFrameFormulas. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3. 2. 1 FrameandCoframe. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 3. 2. 2 Metric. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3. 2. 3 Connection. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3. 2. 4 Curvature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32 3. 3 (n+1)-SplittingAdaptedtoSpaceSlices . . . . . . . . . . . . . . . . . . . . . 33 3. 3. 1 De'nitions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3. 3. 2 StructureCoe'cients. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 3. 3. 3 SplittingoftheConnection . . . . . . . . . . . . . . . . . . . . . . . . . .
 

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Contents

Is Nature Generic?
3
Evolution of Ideas in Modern Cosmology
16
Constraints and Evolution in Cosmology
29
Cosmological Singularities
59
Exact Cosmological Solutions
95
Introduction to Cosmological Dynamical Systems
111
The Quest for the Cosmological Parameters
144
Modern Cosmological Observations
208
Cosmological Perturbations
223
A Particle Theorists Viewpoint
262
An Introduction to Particle Physics
285
Quantum Cosmology
318
Inflationary Cosmology
351
String Cosmology
392
Brane Cosmology
458
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