COSMOLOGY The Origin and Evolution of Cosmic Structure Peter COLES Astronomy Unit, Queen Mary & Westfield College, University of London, United Kingdom Francesco LUCCHIN Dipartimento di Astronomia, Universita di Padova, Italy JOHN WILEY & SONS Chichester New York Brisbane Toronto Singapore
Contents Preface General References: Textbooks xi xix PART I: Cosmological Models 1 The Relativistic Universe 2 1.1 Introduction to General Relativity 2 1.2 The Cosmological Principle 6 1.3 The Robertson-Walker Metric 7 1.4 The Hubble Law 12 1.5 Redshift 15 1.6 The Deceleration Parameter 17 1.7 Cosmological Distances 18 1.8 The M-Z and N-Z Relations 19 1.9 The Friedmann Equations 22 1.10 A Newtonian Approach 23 1.11 The Cosmological Constant 25 1.12 Friedmann Models 28 References 29 2 The Friedmann Models 31 2.1 Perfect Fluid Models / 31 2.2 The Einstein-de Sitter Model 34 2.3 General Properties of Curved Models 36 2.4 Dust Models 38 2.5 Radiative Models 41 2.6 Evolution of the Density Parameter 43 2.7 Cosmological Horizons 44
vi CONTENTS References 46 3 Alternative Cosmologies: Past and Present 47 3.1 Introduction 47 3.2 Hierarchical Cosmologies 48 3.3 Olbers Paradox 48 3.4 The Steady State Model 50 3.5 The Dirac Theory 52 3.6 Brans-Dicke Theory 54 3.7 Hoyle-Narlikar (Conformal) Gravity 56 3.8 The Anthropic Cosmological Principle 57 References 59 4 Observational Properties of the Universe 60 4.1 Introduction 60 4.2 The Hubble Constant 71 4.3 The Distance Ladder 73 4.4 The Age of the Universe 77 4.5 The Density of the Universe 81 4.6 Deviations from the Hubble Expansion 86 4.7 "Classical Cosmology" 89 4.8 The Cosmic Microwave Background 91 References 94 PART II: Evolution of the Big Bang Model 5 Physical Properties of the Hot Big Bang 96 5.1 The Standard Hot Big Bangi 96 5.2 Recombination and Decoupling 98 5.3 Matter-Radiation Equivalence 99 5.4 Thermal History of the Universe 100 5.5 Radiation Entropy per Baryon 102 5.6 Time Scales in the Standard Model 104 References 106 6 The Big Bang and Quantum Gravity 107 6.1 The Big Bang Singularity 107 6.2 The Planck Time 110 6.3 The Planck Era 112 6.4 Quantum Cosmology 114 References 117
CONTENTS vii 7 Phase Transitions and Inflation 118 7.1 The Hot Big Bang 118 7.2 Fundamental Interactions 120 7.3 The Physics of Phase Transitions 122 7.4 Cosmological Phase Transitions 126 7.5 Problems of the Standard Model 129 7.6 The Monopole Problem 130 7.7 The Cosmological Constant Problem 133 7.8 The Cosmological Horizon Problem 135 7.9 The Cosmological Flatness Problem 141 7.10 The Inflationary Universe 145 7.11 Types of Inflation 151 7.12 Successes and Problems of Inflation 154 References 155 8 The Hadron and Lepton Eras 157 8.1 The Quark-Hadron Transition 157 8.2 Chemical Potentials 158 8.3 The Lepton Era 161 8.4 Neutrino Decoupling 163 8.5 The Cosmic Neutrino Background 163 8.6 Cosmological Nucleosynthesis 166 8.7 Non-Standard Nucleosynthesis 173 References 175 9 The Plasma Era 177 9.1 The Radiative Era 177 9.2 The Plasma Epoch 178 9.3 Hydrogen Recombination 180 9.4 The Matter Era 182 9.5 Evolution of the CMB Spectrum 184 References 187 PART III: Structure Formation by Gravitational Instability 10 Introduction to Jeans Theory 190 10.1 Gravitational Instability 190 10.2 Jeans Theory 191 10.3 Jeans Instability in Collisionless Fluids 195 10.4 Jeans Theory in Cosmology 197 References 201
viii CONTENTS 11 Jeans Instability in Friedmann Models 202 11.1 Introduction: an Approximate Analysis 202 11.2 Newtonian Theory in a Dust Universe 204 11.3 Solutions for the Flat Dust Case 207 11.4 The Growth Factor 209 11.5 Solution for Radiation-Dominated Universes 210 11.6 The Method of Autosolution 212 11.7 The Meszaros Effect 215 11.8 Relativistic Solutions 217 References 218 12 The Origin of Structure I: Baryons Only 220 12.1 Introduction 220 12.2 Adiabatic and Isothermal Perturbations 221 12.3 Evolution of the Sound Speed 222 12.4 Evolution of the Jeans Mass 223 12.5 Evolution of the Horizon Mass 225 12.6 Dissipation of Acoustic Waves 226 12.7 Dissipation of Adiabatic Perturbations 229 12.8 Radiation Drag 232 12.9 A Two-Fluid Model 234 12.10 The Kinetic Approach 237 12.11 Structure Formation 241 References 245 13 The Origin of Structure II: Non Baryonic Matter... 246 13.1 Introduction 246 13.2 The Boltzmann Equation for Cosmic Relics 247 13.3 Hot Thermal Relics 248 13.4 Cold Thermal Relics 251 13.5 The Jeans Mass and the Free-Streaming Mass 252 13.6 Structure Formation 257 13.7 Problems and Other Scenarios.* 261 References 263 14 Cosmological Perturbations 264 14.1 Introduction 264 14.2 The Perturbation Spectrum 265 14.3 The Mass Variance 268 14.4 Types of Primordial Spectra 273 14.5 Spectra at Horizon-Crossing - 277 14.6 Fluctuations from Inflation 278 14.7 The Transfer Function 281
CONTENTS ix 14.8 Gaussian Density Perturbations 284 14.9 Covariance Functions 286 14.10 Non-Gaussian Fluctuations? 290 References 292 15 Non Linear Evolution of Perturbations 294 15.1 The Spherical "Top Hat" Collapse 294 15.2 The Zel'dovich Approximation 297 15.3 The Adhesion Model 302 15.4 Self-Similar Evolution 304 15.5 The Mass Function 308 15.6 N-Body Simulations 311 15.7 Hydrodynamics and Dissipation 317 15.8 Biased Galaxy Formation 322 15.9 Angular Momentum and Morphology of Galaxies 326 15.10 Comments 328 References 329 PART IV: Observational Tests 16 Statistics of Galaxy Clustering 332 16.1 Introduction 332 16.2 Correlation Functions: Definitions 334 16.3 The Limber Equations 337 16.4 Correlation Functions: Results 340 16.5 Cluster Correlations and Biasing 345 16.6 Counts in Cells 348 16.7 The Power Spectrum, 351 16.8 Fractal Analysis 354 16.9 Percolation Analysis 357 16.10 Topology 359 16.11 Comments 362 References 364 17 The Cosmic Microwave Background 365 17.1 Introduction 365 17.2 The Angular Power Spectrum 366 17.3 The CMB Dipole 371 17.4 Large Angular Scales 374 17.5 Intermediate Scales 381 17.6 Smaller Scales: Extrinsic Effects 385 17.7 The Sunyaev-ZePdovich Effect 389
x CONTENTS 17.8 Prospects for the Future? 391 References 392 18 Peculiar Motions of Galaxies 393 18.1 Velocity Perturbations 393 18.2 Velocity Correlations 396 18.3 Bulk Flows 399 18.4 Velocity-Density Reconstruction 401 18.5 Redshift-Space Distortions 404 18.6 Implications for fl 406 References 408 19 The Post-Recombination Universe 409 19.1 Introduction 409 19.2 High-Redshift Objects 410 19.3 The Intergalactic Medium 412 19.4 The Infra-Red Background and Dust : 419 19.5 Number-Counts Revisited 422 19.6 The Epoch of Galaxy Formation? 426 19.7 Concluding Remarks 431 References 432 Index 433