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

Cover

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

ISBN 3540437789

Preface

Table of Contents

List of Contributors

1 Is Nature Generic?

1.1 Introduction
1.2 Principles of Cosmological Modelling
1.2.1 Spacetimes
1.2.2 Theories of Gravity
1.3 Cosmologies
1.4 Cosmological Problems
1.4.1 The Singularity Problem
1.4.2 The Problem of Cosmic Topology
1.4.4 Gravity Theories and the Early Universe
1.5 Outlook
References

2 Evolution of Ideas in Modern Cosmology

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

3 Constraints and Evolution in Cosmology

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 Definitions
3.3.2 Structure Coe.cients
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 Rij =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 = (E, H, D, B, g, K, G)
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

4 Cosmological Singularities

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

5 Exact Cosmological Solutions

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 . H Plane
5.4 Homogeneous Anisotropic Models
5.4.1 The Bianchi Classification
5.4.2 Metric Forms
5.4.4 The Nature of the Initial Singularity
5.5 Epilogue
References

6 Introduction to Cosmological Dynamical Systems

6.1 Introduction
6.2 Oneand 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
6.5.4 Stability
References

7 The Quest for the Cosmological Parameters

7.1 Background and Prerequisites
7.1.1 Basic Elements of Dynamical Cosmology
7.1.2 Thermal Beginning of the Universe
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 Affecting Distance Determinations
7.2.4 The Value of H. 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
References

8 Modern Cosmological Observations

8.1 Galaxies
8.1.1 Introduction
8.1.2 Some Cosmological Applications of Galactic Dynamics
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
8.3 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

9 Cosmological Perturbations

9.1 Introduction
9.2 Linear Newtonian Perturbations
9.2.1 The General Fluid Equations
9.2.2 The Unperturbed Background
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
9.4.4 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
9.5.4 Dissipative Effects
9.5.5 Scenarios, Successes and Shortcomings
9.6 Discussion
References

10 Dark Matter: A Particle Theorist's Viewpoint

10.1 Introduction
10.1.1 Einstein Equations
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

11 An Introduction to Particle Physics

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

12 Quantum Cosmology

12.1 Introduction
12.2 Elements of Constrained Dynamics
12.2.1 Introduction
12.2.2 The Hamiltonian Approach
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 Simplification of Einstein's Equations
12.4.2 Automorphisms, Invariant Description of 3-Spaces,
References

13 Inflationary Cosmology

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 In.aton
13.7 Decay of the In.aton
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
References

14 String Cosmology

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
14.2.4 Kaluza-Klein Compactification
14.2.5 Strings in Background Fields
14.2.6 Conformal Invariance and Background Fields
14.2.7 General Methods for Computing -Functions
14.3 String Cosmology
14.3.1 An Expanding Universe in String Theory
14.3.2 String Loop Corrections
14.3.3 De Sitter Universes and Pre-big Bang Scenaria:
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:
14.4.2 Cosmological Backgrounds in String Theory
14.4.4 Liouville String Universe
14.4.5 No Scattering Matrix for Liouville Strings
14.4.6 Graceful Exit from Inflation in Liouville Strings
14.5 Conclusions
References

15 Brane Cosmology

15.1 Introduction
15.2 A Surface S Embedded in a D-Dimensional Manifold M
15.2.1 Elementary Geometry
15.2.2 The Embedding Procedure
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