Cosmology The Origin and Evolution of Cosmic Structure Second Edition Peter Coles School of Physics & Astronomy, University of Nottingham, UK Francesco Lucchin Dipartimento di Astronomia, Università di Padova, Italy www.com Cosmology The Origin and Evolution of Cosmic Structure www.com Cosmology The Origin and Evolution of Cosmic Structure Second Edition Peter Coles School of Physics & Astronomy, University of Nottingham, UK Francesco Lucchin Dipartimento di Astronomia, Università di Padova, Italy www.com Copyright © 2002 John Wiley & Sons, Ltd Baffins Lane, Chichester, West Sussex PO19 1UD, England National 01243 779777 International (+44) 1243 779777 e-mail (for orders and customer service enquiries): cs-books@wiley.uk Visit our Home Page on http://www.com or http://www.com All Rights Reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, scanning or otherwise, except under the terms of the Copyright, Designs and Patents Act 1988 or under the terms of a licence issued by the Copyright Licensing Agency Ltd, 90 Tottenham Court Road, London, UK W1P 0LP, without the permission in writing of the Publisher with the exception of any material supplied specifically for the purpose of being entered and executed on a computer system for exclusive use by the purchaser of the publication. Neither the author nor John Wiley & Sons, Ltd accept any responsibility or liability for loss or damage occasioned to any person or property through using the material, instructions, methods or ideas contained herein, or acting or refraining from acting as a result of such use. The author and publisher expressly disclaim all implied warranties, including mer- chantability or fitness for any particular purpose.
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Library of Congress Cataloging-in-Publication Data (applied for) British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0 471 48909 3 Typeset in 9.5pt Lucida Bright by T&T Productions Ltd, London. Printed and bound in Great Britain by Antony Rowe Ltd. This book is printed on acid-free paper responsibly manufactured from sustainable forestry in which at least two trees are planted for each one used for paper production.com Contents Preface to First Edition xi Preface to Second Edition xix PART 1 Cosmological Models 1 1 First Principles 3 1.1 The Cosmological Principle 3 1.2 Fundamentals of General Relativity 6 1.3 The Robertson–Walker Metric 9 1.4 The Hubble Law 13 1.6 The Deceleration Parameter 17 1.8 The m–z and N–z Relations 20 1.10 The Friedmann Equations 23 1.12 The Cosmological Constant 26 1.13 Friedmann Models 29 2 The Friedmann Models 33 2.1 Perfect Fluid Models 33 2.3 Curved Models: General Properties 38 2.6 Evolution of the Density Parameter 44 2.8 Models with a Cosmological Constant 49 www.com vi Contents 3 Alternative Cosmologies 51 3.1 Anisotropic and Inhomogeneous Cosmologies 52 3.1 The Bianchi models 52 3.2 The Steady-State Model 57 3.3 The Dirac Theory 59 3.4 Brans–Dicke Theory 61 3.6 Hoyle–Narlikar (Conformal) Gravity 64 4 Observational Properties of the Universe 67 4.3 Active galaxies and quasars 70 4.2 The Hubble Constant 75 4.3 The Distance Ladder 79 4.4 The Age of the Universe 83 4.2 Stellar and galactic ages 84 4.5 The Density of the Universe 86 4.1 Contributions to the density parameter 86 4.3 Clusters of galaxies 89 4.6 Deviations from the Hubble Expansion 92 4.8 The Cosmic Microwave Background 100 PART 2 The Hot Big Bang Model 107 5 Thermal History of the Hot Big Bang Model 109 5.1 The Standard Hot Big Bang 109 5.2 Recombination and Decoupling 111 5.3 Matter–Radiation Equivalence 112 5.4 Thermal History of the Universe 113 5.5 Radiation Entropy per Baryon 115 5.6 Timescales in the Standard Model 116 6 The Very Early Universe 119 6.1 The Big Bang Singularity 119 6.2 The Planck Time 122 6.3 The Planck Era 123 6.5 String Cosmology 128 7 Phase Transitions and Inflation 131 7.1 The Hot Big Bang 131 7.3 Physics of Phase Transitions 136 7.4 Cosmological Phase Transitions 138 www.com Contents vii 7.5 Problems of the Standard Model 141 7.6 The Monopole Problem 143 7.7 The Cosmological Constant Problem 145 7.8 The Cosmological Horizon Problem 147 7.2 The inflationary solution 149 7.9 The Cosmological Flatness Problem 152 7.2 The inflationary solution 154 7.10 The Inflationary Universe 156 7.11 Types of Inflation 160 7.1 Old inflation 160 7.2 New inflation 161 7.3 Chaotic inflation 161 7.4 Stochastic inflation 162 7.5 Open inflation 162 7.12 Successes and Problems of Inflation 163 7.13 The Anthropic Cosmological Principle 164 8 The Lepton Era 167 8.1 The Quark–Hadron Transition 167 8.3 The Lepton Era 171 8.5 The Cosmic Neutrino Background 173 8.2 The standard nucleosynthesis model 177 8.3 The neutron–proton ratio 178 8.4 Nucleosynthesis of Helium 179 8.10 Observations versus theory 185 8.7 Non-standard Nucleosynthesis 186 9 The Plasma Era 191 9.1 The Radiative Era 191 9.2 The Plasma Epoch 192 9.4 The Matter Era 195 9.5 Evolution of the CMB Spectrum 197 PART 3 Theory of Structure Formation 203 10 Introduction to Jeans Theory 205 10.2 Jeans Theory for Collisional Fluids 206 10.3 Jeans Instability in Collisionless Fluids 210 10.4 History of Jeans Theory in Cosmology 212 10.5 The Effect of Expansion: an Approximate Analysis 213 10.6 Newtonian Theory in a Dust Universe 215 10.7 Solutions for the Flat Dust Case 218 10.8 The Growth Factor 219 www.com viii Contents 10.9 Solution for Radiation-Dominated Universes 221 10.10 The Method of Autosolution 223 10.11 The Meszaros Effect 225 10.12 Relativistic Solutions 227 11 Gravitational Instability of Baryonic Matter 229 11.2 Adiabatic and Isothermal Perturbations 230 11.3 Evolution of the Sound Speed and Jeans Mass 231 11.4 Evolution of the Horizon Mass 233 11.5 Dissipation of Acoustic Waves 234 11.6 Dissipation of Adiabatic Perturbations 237 11.8 A Two-Fluid Model 241 11.9 The Kinetic Approach 244 11.10 Summary 248 12 Non-baryonic Matter 251 12.2 The Boltzmann Equation for Cosmic Relics 252 12.3 Hot Thermal Relics 253 12.4 Cold Thermal Relics 255 12.5 The Jeans Mass 256 12.1 Hot Dark Matter 260 12.2 Cold Dark Matter 261 12.3 Summary 262 13 Cosmological Perturbations 263 13.2 The Perturbation Spectrum 264 13.3 The Mass Variance 266 13.1 Mass scales and filtering 266 13.2 Properties of the filtered field 268 13.3 Problems with filters 270 13.4 Types of Primordial Spectra 271 13.5 Spectra at Horizon Crossing 275 13.6 Fluctuations from Inflation 276 13.7 Gaussian Density Perturbations 279 13.9 Non-Gaussian Fluctuations? 284 14 Nonlinear Evolution 287 14.1 The Spherical ‘Top-Hat’ Collapse 287 14.2 The Zel’dovich Approximation 290 14.3 The Adhesion Model 294 14.4 Self-similar Evolution 296 14.3 Scaling of the power spectrum 300 14.5 The Mass Function 301 14.2 Particle–mesh techniques 306 14.4 Initial conditions and boundary effects 309 www.com Contents ix 14.8 Biased Galaxy Formation 314 14.10 Comments 321 15 Models of Structure Formation 323 15.3 Gravitational Instability in Brief 326 15.4 Primordial Density Fluctuations 327 15.5 The Transfer Function 328 15.6 Beyond Linear Theory 330 15.7 Recipes for Structure Formation 331 15.8 Comments 334 PART 4 Observational Tests 335 16 Statistics of Galaxy Clustering 337 16.3 The Limber Equation 342 16.4 Correlation Functions: Results 344 16.1 Two-point correlations 344 16.5 The Hierarchical Model 346 16.6 Cluster Correlations and Biasing 350 16.7 Counts in Cells 352 16.8 The Power Spectrum 355 16.12 Comments 365 17 The Cosmic Microwave Background 367 17.2 The Angular Power Spectrum 368 17.3 The CMB Dipole 371 17.4 Large Angular Scales 374 17.1 The Sachs–Wolfe effect 374 17.2 The COBE DMR experiment 377 17.3 Interpretation of the COBE results 379 17.6 Smaller Scales: Extrinsic Effects 385 17.7 The Sunyaev–Zel’dovich Effect 389 17.8 Current Status 391 18 Peculiar Motions of Galaxies 393 18.4 Velocity–Density Reconstruction 400 18.5 Redshift-Space Distortions 402 18.6 Implications for Ω0 405 www.com x Contents 19 Gravitational Lensing 409 19.2 Basic Gravitational Optics 412 19.3 More Complicated Systems 415 19.3 Arcs, arclets and cluster masses 420 19.4 Weak lensing by large-scale structure 421 19.5 The Hubble constant 422 19.5 Comments 423 20 The High-Redshift Universe 425 20.3 The Intergalactic Medium (IGM) 428 20.2 The Gunn–Peterson test 428 20.3 Absorption line systems 430 20.4 X-ray gas in clusters 432 20.5 Spectral distortions of the CMB 432 20.6 The X-ray background 433 20.4 The Infrared Background and Dust 434 20.5 Number-counts Revisited 437 20.6 Star and Galaxy Formation 438 20.7 Concluding Remarks 444 21 A Forward Look 447 21.3 X-rays and the Hot Universe 449 21.4 The Apotheosis of Astrometry: GAIA 450 21.5 The Next Generation Space Telescope: NGST 452 21.6 Extremely Large Telescopes 453 21.7 Far-IR and Submillimetre Views of the Early Universe 454 21.8 The Cosmic Microwave Background 456 21.9 The Square Kilometre Array 456 21.11 Sociology, Politics and Economics 460 21. Physical Constants 463 Appendix B.
Useful Astronomical Quantities 465 Appendix C. Particle Properties 467 References 469 Index 485 www.com Preface to First Edition This is a book about modern cosmology. Because this is a big subject – as big as the Universe – we have had to choose one particular theme upon which to focus our treatment. Current research in cosmology ranges over fields as diverse as quantum gravity, general relativity, particle physics, statistical mechanics, nonlin- ear hydrodynamics and observational astronomy in all wavelength regions, from radio to gamma rays.
We could not possibly do justice to all these areas in one volume, especially in a book such as this which is intended for advanced under- graduates or beginning postgraduates. Because we both have a strong research interest in theories for the origin and evolution of cosmic structure – galaxies, clusters and the like – and, in many respects, this is indeed the central problem in this field, we decided to concentrate on those elements of modern cosmology that pertain to this topic. We shall touch on many of the areas mentioned above, but only insofar as an understanding of them is necessary background for our analysis of structure formation. Cosmology in general, and the field of structure formation in particular, has been a ‘hot’ research topic for many years.
Recent spectacular observational break- throughs, like the discovery by the COBE satellite in 1992 of fluctuations in the temperature of the cosmic microwave background, have made newspaper head- lines all around the world. Both observational and theoretical sides of the subject continue to engross not only the best undergraduate and postgraduate students and more senior professional scientists, but also the general public. Part of the fascination is that cosmology lies at the crossroads of many disciplines. An intro- duction to this subject therefore involves an initiation into many seemingly dis- parate branches of physics and astrophysics; this alone makes it an ideal area in which to encourage young scientists to work.
Nevertheless, cosmology is a peculiar science. The Universe is, by definition, unique. We cannot prepare an ensemble of universes with slightly different param- eter values and look for differences or correlations in their behaviour. In many branches of physical science such experimentation often leads to the formulation of empirical laws which give rise to models and subsequently theories.
Cosmol- ogy is different. We have only one Universe, and this must provide the empirical laws we try to explain by theory, as well as the experimental evidence we use to test the theories we have formulated. Though the distinction between them is, of course, not completely sharp, it is fair to say that physics is predominantly char- acterised by experiment and theory, and cosmology by observation and paradigm.