The physics of the early universe : [review talks given in the Second Aegean School on the Early Universe, held in Ermoupolis on Syros Island, Greece, in September 22-30, 2003

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. Cosmology String Theory,Dark Matter Title 3 Preface 6 Contents 10 1. An Introduction to the Physics-of the Early Universe 16 1.1 The Hubble Law 16 1.2 Comoving Coordinates and the Scale Factor 17 1.3 The Cosmic Microwave Background 19 1.4 The Friedmann Models 21 1.5 Simple Cosmological Solutions 24 1.5.1 Empty de Sitter Universe 24 1.5.2 Vacuum Energy Dominated Universe 24 1.5.3 Radiation Dominated Universe 25 1.5.4 Matter Dominated Universe 26 1.5.5 General Equation of State 27 1.5.6 The E.ects of Curvature 28 1.5.7 The E.ects of a Cosmological Constant 29 1.6 The Matter Density in the Universe 29 1.7 The Standard Cosmological Model 30 1.7.1 Thermal History 31 1.7.2 Nucleosynthesis 32 1.8 Problems of Standard Cosmology 33 1.8.1 The Horizon Problem 33 1.8.2 The Coincidence Puzzle and the Flatness Problem 35 1.9 Phase Transitions in the Early Universe 36 1.10 In.ation 38 1.11 The Baryon Asymmetry in the Universe 40 Acknowledgements 41 2. Cosmological Perturbation Theory 43 2.1 Introduction 43 2.2 The Background 44 2.3 Gauge Invariant Perturbation Variables 45 2.3.1 Gauge Transformation, Gauge Invariance 46 2.3.2 Harmonic Decomposition of Perturbation Variables 47 2.3.3 Metric Perturbations 49 2.3.4 Perturbations of the Energy Momentum Tensor 51 2.4 Einstein’s Equations 53 2.4.1 Constraint Equations 53 2.4.2 Dynamical Equations 53 2.4.3 Energy Momentum Conservation 53 2.4.4 A Special Case 54 2.5 Simple Examples 55 2.5.1 The Pure Dust Fluid for κ = 0, Λ = 0 55 2.5.2 The Pure Radiation Fluid, κ = 0, Λ = 0 58 2.5.3 Adiabatic Initial Conditions 59 2.6 Scalar Field Cosmology 61 2.7 Generation of Perturbations During In.ation 63 2.7.1 Scalar Perturbations 63 2.7.2 Vector Perturbations 65 2.7.3 Tensor Perturbations 66 2.8 Lightlike Geodesics and CMB Anisotropies 67 2.9 Power Spectra 70 2.10 Some Remarks on Perturbation Theory in Braneworlds 76 2.11 Conclusions 79 Acknowledgements 80 3. Cosmic Microwave Background Anisotropies 82 3.1 Introduction 82 3.2 Fundamentals of CMB Physics 83 3.2.1 Thermal History and Recombination 83 3.2.5 Other Features of the Temperature-Anisotropy Power Spectrum 97 3.2.3 Kinetic Theory 85 3.2.4 Photon–Baryon Dynamics 90 3.2.2 Statistics of CMB Anisotropies 84 3.3 Cosmological Parameters and the CMB 101 3.3.1 Matter and Baryons 102 3.3.2 Curvature, Dark Energy and Degeneracies 103 3.4 CMB Polarization 105 3.4.1 Polarization Observables 105 3.4.2 Physics of CMB Polarization 106 3.5 Highlights of Recent Results 108 3.5.1 Detection of CMB Polarization 108 3.5.2 Implications of Recent Results for In.ation 110 3.5.3 Detection of Late-Time Integrated Sachs–Wolfe E.ect 111 3.6 Conclusions 111 Acknowledgments 113 4. Observational Cosmology 115 4.1 Introduction 115 4.2 Astronomy Made Simple (for Physicists) 117 4.3 Basics of FRW Cosmology 119 4.4 Observational Support for the Standard Model of the Early Universe 122 4.5 The Post-recombination Universe: Determination of Ho and to 127 4.6 Looking for Discordance: The Classical Tests 131 4.6.1 The Angular Size Test 131 4.6.2 The Modern Angular Size Test: CMB-ology 132 4.6.3 The Flux-Redshift Test: Supernovae Ia 135 4.6.4 Number Counts of Faint Galaxies 139 4.7 Conclusions 143 Acknowledgements 145 5. Dark Matter and Dark Energy 148 5.1 Dark Matter 148 5.2 Dark Energy 157 5.2.1 The Cosmological Constant and Vacuum Energy 157 5.2.2 Dynamical Models of Dark Energy 160 5.2.3 Quintessence 165 5.2.4 Dark Energy in Braneworld Models 168 5.2.5 Chaplygin Gas 171 5.2.6 Is Dark Energy a Phantom? 172 5.2.7 Reconstructing Dark Energy and the State.nder Diagnostic 174 5.2.8 Big Rip, Big Crunch or Big Horizon? – The Fate of the Universe in Dark Energy Models 177 5.3 Conclusions and Future Directions 179 Acknowledgements 180 6. String Cosmology 187 6.1 Introduction 187 6.2 M-Theory Basics 188 6.2.1 The Main Players 188 6.2.2 Branes 191 6.2.3 Compacti.cation 193 6.2.4 The Four-Dimensional E.ective Theory 195 6.2.5 A Speci.c Example: Heterotic M-Theory 198 6.3 Classes of Simple Time-Dependent Solutions 201 6.3.1 Rolling Radii Solutions 201 6.3.2 Including Axions 203 6.3.3 Moving Branes 204 6.3.4 Duality Symmetries and Cosmological Solutions 205 6.4 M-Theory and In.ation 206 6.4.1 Reminder In.ation 206 6.4.2 Potential-Driven In.ation 207 6.4.3 Pre-Big-Bang In.ation 208 6.5 Topology Change in Cosmology 210 6.5.1 M-Theory Flops 211 6.5.2 Flops in Cosmology 212 6.6 Conclusions 214 Acknowledgements 214 7. Brane-World Cosmology 218 7.1 Introduction 218 7.2 Randall-Sundrum Brane-Worlds 221 7.3 Covariant Generalization of RS Brane-Worlds 225 7.3.1 Field Equations on the Brane 225 7.3.2 The Brane Observer’s Viewpoint 228 7.3.3 Conservation Equations: Ordinary and “Weyl” Fluids 230 7.4 Brane-World Cosmology: Dynamics 233 7.5 Brane-World In.ation 235 7.6 Brane-World Cosmology: Perturbations 239 7.6.1 Metric-Based Perturbations 240 7.6.2 Curvature Perturbations and the Sachs–Wolfe E.ect 242 7.7 Gravitational Wave Perturbations 244 7.8 Brane-World CMB Anisotropies 247 7.9 Conclusions 252 Acknowledgments 254 8. Gravitational Wave Astronomy:-The High Frequency Window 258 8.1 Introduction 258 8.2 Einstein’s Elusive Waves 260 8.2.1 The Nature of the Waves 261 8.2.2 Estimating the Gravitational-Wave Amplitude 264 8.3 High-Frequency Gravitational Wave Sources 268 8.3.1 Radiation from Binary Systems 269 8.3.2 Gravitational Collapse 269 8.3.3 Rotational Instabilities 271 8.3.4 Bar-Mode Instability 272 8.3.5 CFS Instability, f- and r-Modes 273 8.3.6 Oscillations of Black Holes and Neutron Stars 275 8.4 Gravitational Waves of Cosmological Origin 276 Acknowledgements 278 9. Computational Black Hole Dynamics 280 9.1 Introduction 280 9.2 Einstein Equation and Numerical Relativity 281 9.3 Black Hole Horizons and Excision 290 9.4 Initial Data and the Kerr-Schild Metric 293 9.5 Black Hole Evolutions 295 9.6 Conclusions and Future Work 297 Acknowledgments 298 Index 302 "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 particular 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."--Jacket 1 An Introduction to the Physics of the Early Universe....Pages 3-29 2 Cosmological Perturbation Theory....Pages 31-69 3 Cosmic Microwave Background Anisotropies....Pages 71-103 4 Observational Cosmology....Pages 105-137 5 Dark Matter and Dark Energy....Pages 141-179 6 String Cosmology....Pages 181-211 7 Brane-World Cosmology....Pages 213-252 8 Gravitational Wave Astronomy:The High Frequency Window....Pages 255-276 9 Computational Black Hole Dynamics....Pages 277-298