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 . . . . . . . . . . . . . . . . . . . . . . . . . .

lgrsnf/Cotsakis S., Papantonopoulos E. (eds.) Cosmological Crossroads (LNP0592, Springer, 2002)(ISBN 9783540437789)(T)(O)(468s).djvu

Aegean Summer School on Cosmology (1st 2001 Samos Island, Greece)

Aegean Summer School; Aegean Summer School on Cosmology

S. Cotsakis, E. Papantonopoulos (eds.)

Springer Spektrum. in Springer-Verlag GmbH

Steinkopff. in Springer-Verlag GmbH

Lecture notes in physics -- 592., Berlin, New York, Germany, 2002

1 edition, December 16, 2002

Germany, Germany

"Edited version of the lectures delivered during the 1st Aegean Summer School on Cosmology, held on Samos island, Greece, in September 21-29, 2001"--P. [v].
Includes bibliographical references.

Chapter 1
1.1 Introduction
1.2 Principles of Cosmological Modelling
1.2.1 Spacetimes
1.2.2 Theories of Gravity
1.2.3 Matter Fields
1.3 Cosmologies
1.4 Cosmological Problems
1.4.1 The Singularity Problem
1.4.2 The Problem of Cosmic Topology
1.4.3 The Problem of Asymptotic States
1.4.4 Gravity Theories and the Early Universe
1.5 Outlook
Acknowledgements
References
Chapter 2
2.1 Introduction
2.2 The Beginnings of Modern Cosmology (1917–1950)
2.3 Cosmology 1950–1970: Hot Big Bang, Singularities and Quantum Approach
2.4 Cosmology 1970–1990: Chaotic, Inflationary, Quantum and Alternative
2.5 Conclusions and Outlook
References
Chapter 3
3.1 Introduction
3.2 Moving Frame Formulas
3.2.1 Frame and Coframe
3.2.2 Metric
3.2.3 Connection
3.2.4 Curvature
3.3 (n+1)-Splitting Adapted to Space Slices
3.3.1 De.nitions
3.3.2 Structure Coeffcients
3.3.3 Splitting of the Connection
3.3.4 Splitting of the Riemann Tensor
3.4 Constraints and Evolution
3.5 Analytic Cauchy Problem
3.6 Non-strict Hyperbolicity of R_{ij} = 0
3.7 Wave Equation for K, Hyperbolic System
3.8 Hyperbolic-Elliptic System
3.9 Local Existence and Uniqueness
3.10 First Order Hyperbolic Systems
3.10.1 FOSH Systems
3.10.2 Other First Order Hyperbolic Systems
3.11 Bianchi-Einstein Equations
3.11.1 Wave Equation for the Riemann Tensor
3.11.2 Case n=3, FOS System
3.11.3 Cauchy Adapted Frame
3.11.4 FOSH system for u equiv (E, H, D, B, =g, K, =Gamma)
3.11.5 Elliptic - Hyperbolic System
3.12 Bel-Robinson Energy
3.12.1 Bel-Robinson Energy in a Strip
3.12.2 Local Energy Estimate
3.13 (n+1)-Splitting in a Time-Adapted Frame
3.13.1 Metric and Coframe
3.13.2 Splitting of Connection
3.13.3 Splitting of Curvature
3.13.4 Bianchi Equations (Case n=3)
3.13.5 Vacuum Case
3.13.6 Perfect Fluid
3.13.7 Conclusion
References
Chapter 4
4.1 Introduction
4.2 Cosmologies
4.3 The Spacetime Metric
4.4 Derivatives
4.5 Transport and Geodesics
4.6 Conjugate Points and Geodesic Congruences
4.7 Causal Geometry
4.8 Globalization and Singularity Theorems
4.9 Cosmological Applications
References
Chapter 5
5.1 Introduction: Mental Pictures of the Universe
5.2 Basic Assumptions and Their Implications
5.2.1 Assumptions
5.2.2 Implications
5.3 Homogeneous Isotropic Models
5.3.1 Metric Forms
5.3.2 Cosmological Redshift
5.3.3 Evolution Equations and Sources
5.3.4 Linear Equation of State
5.3.5 Particular Models
5.3.6 Standard Notation and the Omega- H Plane
5.4 Homogeneous Anisotropic Models
5.4.1 The Bianchi Classi.cation
5.4.2 Metric Forms
5.4.3 Particular Models
5.4.4 The Nature of the Initial Singularity
5.5 Epilogue
References
Chapter 6
6.1 Introduction
6.2 One- and Two-Fluid Isotropic Cosmologies in GR
6.3 Bianchi Models
6.4 Scalar-Tensor Isotropic Cosmologies
6.5 Appendix. Differential Equations. Basic Concepts
6.5.1 Higher-Dimensional Systems
6.5.2 Linearization
6.5.3 Limit Sets, Invariant Sets
6.5.4 Stability
References
Chapter 7
7.1 Background and Prerequisites
7.1.1 Basic Elements of Dynamical Cosmology
7.1.2 Thermal Beginning of the Universe
7.1.3 Cosmological Parameters
7.1.4 Distribution of Matter in the Universe
7.2 Distance Scale, Hubble Constant and the Age of the Universe
7.2.1 Distances of Extragalactic Objects
7.2.2 Biases A.ecting Distance Determinations
7.2.3 Distance Indicators
7.2.4 The Value of H_o and the Age of the Universe
7.3 Determination of the Matter/Energy Density of the Universe
7.3.1 The CMB Fluctuation Spectrum
7.3.2 The Hubble Diagram with SNIa
7.3.3 Clustering of Galaxies, Clusters and QSO’s
7.3.4 M/L Observations
7.3.5 Cluster Baryon Fraction
7.3.6 Large-Scale Velocity Field
7.3.7 Rate of Cluster Formation Evolution
7.4 Summary
Acknowledgments
References
Chapter 8
8.1 Galaxies
8.1.1 Introduction
8.1.2 Some Cosmological Applications of Galactic Dynamics
8.1.3 Redshift Surveys
8.1.4 Number Counts and Galaxy Evolution
8.1.5 High Redshift Galaxies
8.2 Clusters and Groups of Galaxies
8.2.1 Introduction
8.2.2 Surveys for Clusters
8.2.3 The Cosmological Significance of Clusters
8.3 Active Galactic Nuclei
8.3.1 Introduction
8.3.2 AGN Surveys
8.3.3 The AGN Evolution
8.3.4 The AGN Clustering
8.3.5 QSOs as a Probe of the Intergalactic Medium
References
Chapter 9
9.1 Introduction
9.2 Linear Newtonian Perturbations
9.2.1 The General Fluid Equations
9.2.2 The Unperturbed Background
9.2.3The Linear Regime
9.2.4 The Jeans Length
9.2.5 Multi-component Fluids
9.2.6 Solutions
9.2.7 Summary
9.3 Linear Relativistic Perturbations
9.3.1 The Gauge Problem
9.3.2 The Relativistic Equations
9.3.3 The Linear Regime
9.3.4 Solutions
9.3.5 Summary
9.4 Baryonic Structure Formation
9.4.1 Adiabatic and Isothermal Perturbations
9.4.2 Evolution of the Sound Speed
9.4.3 Evolution of the Jeans Length and the Jeans Mass
9.4.4 Evolution of the Hubble Mass
9.4.5 Dissipative Effects
9.4.6 Scenarios and Problems
9.5 Non-baryonic Structure Formation
9.5.1 Non-baryonic Cosmic Relics
9.5.2 Evolution of the Jeans Mass
9.5.3 Evolution of the Hubble Mass
9.5.4 Dissipative Effects
9.5.5 Scenarios, Successes and Shortcomings
9.6 Discussion
Acknowledgements
References
Chapter 10
10.1 Introduction
10.1.1 Einstein Equations in a Friedmann-Robertson-Walker Universe
10.1.2 The Hubble Constant – The Critical Density
10.2 The Thermal Universe
10.2.1 The Thermal Distributions of Particles
10.2.2 The Energy Densities of Photons and Neutrinos
10.3 The Evolution of the Universe
10.3.1 Solving Friedmann’s Equations
10.3.2 “Decoupling” or “Freeze-out” of Particles
10.4 Dark Matter
10.4.1 Evidence for Dark Matter and Dark Energy
10.4.2 Candidates for DM-Supersymmetry
10.5 The Neutralino as the LSP and Its Relic Density
10.5.1 The Neutralino as the LSP
10.5.2 The Boltzmann Transport Equation
10.6 Constraining SUSY-Conclusions
References
Chapter 11
11.1 The Standard Model
11.2 Grand Unification
11.3 Supersymmetry
11.4 The Supersymmetric Standard Model
11.5 Strings
11.6 M-Theory and Duality
References
Chapter 12
12.1 Introduction
12.2 Elements of Constrained Dynamics
12.2.1 Introduction
12.2.2 The Hamiltonian Approach
12.2.3 Quantization of Constrained Systems
12.3 A Pedagogical Example: The Kantowski-Sachs Model
12.3.1 The Classical Case
12.3.2 The Quantum Case
12.4 Automorphisms in Classical and Quantum Cosmology
12.4.1 The Simpli.cation of Einstein’s Equations
12.4.2 Automorphisms, Invariant Description of 3-Spaces, and Quantum Cosmology
Chapter 13
13.1 Introduction
13.2 The Big Bang Model
13.2.1 Hubble Expansion
13.2.2 Friedmann Equation
13.2.3 Important Cosmological Parameters
13.2.4 Particle Horizon
13.2.5 Brief History of the Early Universe
13.3 Shortcomings of Big Bang
13.3.1 Horizon Problem
13.3.2 Flatness Problem
13.3.3 Magnetic Monopole Problem
13.3.4 Density Perturbations
13.4 Inflation
13.4.1 Resolution of the Horizon Problem
13.4.2 Resolution of the Flatness Problem
13.4.3 Resolution of the Monopole Problem
13.5 Detailed Analysis of Inflation
13.6 Coherent Oscillations of the Inflaton
13.7 Decay of the Inflaton
13.8 Density Perturbations from Inflation
13.9 Density Perturbations in ‘Matter’
13.10 Temperature Fluctuations
13.11 Hybrid Inflation
13.11.1 The Non-supersymmetric Version
13.11.2 The Supersymmetric Version
13.12 Extensions of Supersymmetric Hybrid Inflation
13.12.1 Shifted Hybrid Inflation
13.12.2 Smooth Hybrid Inflation
13.13 ‘Reheating’ and the Gravitino Constraint
13.14 Baryogenesis via Leptogenesis
13.14.1 Primordial Leptogenesis
13.14.2 Sphaleron Effects
13.15 Conclusions
Acknowledgements
References
Chapter 14
14.1 Introduction
14.2 Introduction to String Effective Actions
14.2.1 World-Sheet String Formalism
14.2.2 Conformal Invariance and Critical Dimension of Strings
14.2.3 Some Hints Towards Supersymmetric Strings
14.2.4 Kaluza-Klein Compacti.cation
14.2.5 Strings in Background Fields
14.2.6 Conformal Invariance and Background Fields
14.3 String Cosmology
14.3.1 An Expanding Universe in String Theory and the Role of the Dilaton Background
14.3.2 String Loop Corrections and De Sitter (Inflationary) Space Times
14.3.3 De Sitter Universes and Pre-big Bang Scenaria: The Crucial Role of the Dilaton Field
14.3.4 Some Phenomenological Implications of String Cosmology
14.4 Challenges in String Cosmology and Speculations on Their Treatment
14.4.1 Exit from Inflationary Phase: A Theoretical Challenge for String Theory
14.4.2 Cosmological Backgrounds in String Theory and World-Sheet Renormalization-Group Flow
14.4.3 Liouville Strings and Time as a World-Sheet RG Flow Parameter
14.4.4 Liouville String Universe and Time-Dependent Vacuum Energy
14.4.5 No Scattering Matrix for Liouville Strings
14.4.6 Graceful Exit from In.ation in Liouville Strings
14.5 Conclusions
Acknowledgements
References
Chapter 15
15.1 Introduction
15.2.1 Elementary Geometry
15.2.2 The Embedding Procedure
15.2.3 The Israel Matching Conditions
15.3 Brane Cosmology in 5-Dimensional Spacetime
15.3.1 The Einstein Equations on the Brane
15.3.2 Cosmology on the Brane
15.4 Induced Gravity on the Brane
15.4.1 Cosmology on the Brane with a (4)^R Term
15.5 A Brane on the Move
15.5.1 Cosmology of the Moving Brane
15.6 Conclusions
References

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. Is Nature Generic?- Evolution Of Ideas In Modern Cosmology -- Constraints And Evolution In Cosmology -- Cosmological Singularities -- Exact Cosmological Solutions -- Introduction To Cosmological Dynamical Systems -- Cosmological Parameters -- Modern Cosmological Observations -- Cosmological Perturbations -- Dark Matter, A Particle Theorist's Viewpoint -- An Introduction To Particle Physics -- Quantum Cosmology -- Inflationary Cosmology -- String Cosmology -- Brane Cosmology. S. Cotsakis, L. Papantonopoulos (eds.). Includes Bibliographical References.

This textbook has grown out of lectures held at a summer school on cosmology, in response to a need for an advanced text that addresses the needs of both postgraduate students and nonspecialist researchers from various disciplines ranging from mathematical physics to observational astrophysics.

Lecture Notes in Physics
Erscheinungsdatum: 07.11.2002

2024-07-27