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-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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