This book has grown out of lectures held at a summer school on cosmology, in response to an ever increasing need for an advanced textbook that addresses the needs of both postgraduate students and nonspecialist researchers from various disciplines ranging from mathematical physics to observational astrophysics. Bridging the gap between standard textbook material in cosmology and the forefront of research, this book also constitutes a modern source of reference for the experienced researcher in classical and quantum cosmology.

Black Holes are still considered to be among the most mysterious and fascinating objects in our universe. Awaiting the era of gravitational astronomy, much progress in theoretical modeling and understanding of classical and quantum black holes has already been achieved.

The present volume serves as a tutorial, high-level guided tour through the black-hole landscape: information paradox and blackhole thermodynamics, numerical simulations of black-hole formation and collisions, braneworld scenarios and stability of black holes with respect to perturbations are treated in great detail, as is their possible occurrence at the LHC.

An outgrowth of a topical and tutorial summer school, this extensive set of carefully edited notes has been set up with the aim of constituting an advanced-level, multi-authored textbook which meets the needs of both postgraduate students and young researchers in the fields of modern cosmology, astrophysics and (quantum) field theory.

The nature and essence of Dark Matter and Dark Energy have become the central issue in modern cosmology over the past years. This extensive volume, an outgrowth of a topical and tutorial summer school, has been set up with the aim of constituting an advanced-level, multi-authored textbook which meets the needs of both postgraduate students and young researchers in the fields of modern cosmology and astrophysics.

The Physics of the Early Universe is an edited and expanded version of the lectures given at a recent summer school of the same name. Its aim is to present an advanced multi-authored textbook that meets the needs of both postgraduate students and young researchers interested in, or already working on, problems in cosmology and general relativity, with emphasis on the early universe. A particularly strong feature of the present work is the constructive-critical approach to the present mainstream theories, the careful assessment of some alternative approaches, and the overall balance between theoretical and observational considerations. As such, this book will also benefit experienced scientists and nonspecialists from related areas of research.

In the last few years modified gravity theories have been proposed as extensions of Einstein's theory of gravity. Their main motivation is to explain the latest cosmological and astrophysical data on dark energy and dark matter. The study of general relativity at small scales has already produced important results (cf e.g. LNP 863 Quantum Gravity and Quantum Cosmology) while its study at large scales is challenging because recent and upcoming observational results will provide important information on the validity of these modified theories. In this volume, various aspects of modified gravity at large scales will be discussed: high-curvature gravity theories; general scalar-tensor theories; Galileon theories and their cosmological applications; F(R) gravity theories; massive, new massive and topologically massive gravity; Chern-Simons modifications of general relativity (including holographic variants) and higher-spin gravity theories, to name but a few of the most important recent developments. Edited and authored by leading researchers in the field and cast into the form of a multi-author textbook at postgraduate level, this volume will be of benefit to all postgraduate students and newcomers from neighboring disciplines wishing to find a comprehensive guide for their future research.

The AdS/CFT correspondence is a powerful tool in studying strongly coupled phenomena in gauge field theories, using results from a weakly coupled gravity background studied in the realm of sting theory. AdS/CFT was first successfully applied to the study of phenomena such as the quark-gluon plasma produced in heavy ions collisions. Soon it was realized that its applicability can be extended, in a more phenomenological approach, to condensed matter systems and to systems described by fluid dynamics.

The set of tutorial reviews in this volume are intended as an introduction to and survey of principle of the AdS/CFT correspondence in its field/string theoretic formulation, its applicability to holographic QCD and to heavy ions collisions, and to give a first account of processes in fluid dynamics and condensed matter physics, which can be studied with the use of this principle.

Written by leading researchers in the field and cast into the form of a high-level but approachable multi-author textbook, this volume will be of benefit to all postgraduate students, and newcomers from neighboring disciplines wishing to find a comprehensive guide for their future research.

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 ...

The Physics of the Early Universe is an edited and expanded version of the lectures given at a recent summer school of the same name. Its aim is to present an advanced multi-authored textbook that meets the needs of both postgraduate students and young researchers interested in, or already working on, problems in cosmology and general relativity, with emphasis on the early universe. A particularly strong feature of the present work is the constructive-critical approach to the present mainstream theories, the careful assessment of some alternative approaches, and the overall balance between theoretical and observational considerations. As such, this book will also benefit experienced scientists and nonspecialists from related areas of research.