Introduction to Cosmology Third Edition Matts Roos www.com Introduction to Cosmology Third Edition www.com Introduction to Cosmology Third Edition Matts Roos www.com Copyright © 2003 John Wiley & Sons, Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England Telephone (+44) 1243 779777 Email (for orders and customer service enquiries): cs-books@wiley.uk Visit our Home Page on www.com or 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, photocopy- ing, 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 W1T 4LP, UK, without the permission in writing of the Publisher. Requests to the Publisher should be addressed to the Permissions Department, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex PO19 8SQ, England, or emailed to permreq@wiley.uk, or faxed to (+44) 1243 770571. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered.
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Some content that appears in print may not be available in electronic books. Library of Congress Cataloging-in-Publication Data Roos, Matts. Introduction to cosmology / Matt Roos. Includes bibliographical references and index.
ISBN 0-470-84909-6 (acid-free paper) – ISBN 0-470-84910-X (pbk. : acid-free paper) 1.1 — dc22 2003020688 British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library ISBN 0 470 84909 6 (hardback) 0 470 84910 X (paperback) 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 To my dear grandchildren Francis Alexandre Wei Ming (1986) Christian Philippe Wei Sing (1990) Cornelia (1989) Erik (1991) Adrian (1994) Emile Johannes (2000) Alaia Ingrid Markuntytär (2002) www.com Contents Preface to First Edition ix Preface to Second Edition xi Preface to Third Edition xiii 1 From Newton to Hubble 1 1.2 Inertial Frames and the Cosmological Principle 7 1.5 The Age of the Universe 17 1.6 Expansion in a Newtonian World 19 2 Relativity 25 2.1 Lorentz Transformations and Special Relativity 25 2.2 Metrics of Curved Space-time 30 2.3 Relativistic Distance Measures 37 2.4 General Relativity and the Principle of Covariance 45 2.5 The Principle of Equivalence 49 2.6 Einstein’s Theory of Gravitation 54 3 Gravitational Phenomena 61 3.1 Classical Tests of General Relativity 62 3.2 The Binary Pulsar 63 3.5 Gravitational Waves 80 4 Cosmological Models 87 4.1 Friedmann–Lemaître Cosmologies 87 4.2 de Sitter Cosmology 99 4.4 Model Testing and Parameter Estimation.
I 106 Introduction to Cosmology Third Edition by Matts Roos © 2003 John Wiley & Sons, Ltd ISBN 0 470 84909 6 (cased) ISBN 0 470 84910 X (pbk) www.com viii Contents 5 Thermal History of the Universe 113 5.4 The Early Radiation Era 128 5.5 Photon and Lepton Decoupling 132 5.6 Big Bang Nucleosynthesis 139 6 Particles and Symmetries 149 6.3 Hadrons and Quarks 159 6.4 The Discrete Symmetries C, P, T 163 6.5 Spontaneous Symmetry Breaking 166 6.6 Primeval Phase Transitions and Symmetries 171 6.7 Baryosynthesis and Antimatter Generation 178 7 Cosmic Inflation 185 7.1 Paradoxes of the Expansion 186 7.2 ‘Old’ and ‘New’ Inflation 192 7.3 Chaotic Inflation 196 7.4 The Inflaton as Quintessence 202 7.5 Cyclic Models 205 8 Cosmic Microwave Background 211 8.1 The CMB Temperature 212 8.4 Model Testing and Parameter Estimation. II 225 9 Cosmic Structures and Dark Matter 231 9.3 The Evidence for Dark Matter 241 9.4 Dark Matter Candidates 248 9.5 The Cold Dark Matter Paradigm 252 10 Epilogue 259 10.2 Open Questions 262 Tables 267 Index 271 www.com Preface to First Edition A few decades ago, astronomy and particle physics started to merge in the com- mon field of cosmology. The general public had always been more interested in the visible objects of astronomy than in invisible atoms, and probably met cosmol- ogy first in Steven Weinberg’s famous book The First Three Minutes. More recently Stephen Hawking’s A Brief History of Time has caused an avalanche of interest in this subject.
Although there are now many popular monographs on cosmology, there are so far no introductory textbooks at university undergraduate level. Chapters on cosmology can be found in introductory books on relativity or astronomy, but they cover only part of the subject. One reason may be that cosmology is explicitly cross-disciplinary, and therefore it does not occupy a prominent position in either physics or astronomy curricula. At the University of Helsinki I decided to try to take advantage of the great interest in cosmology among the younger students, offering them a one-semester course about one year before their specialization started.
Hence I could not count on much familiarity with quantum mechanics, general relativity, particle physics, astrophysics or statistical mechanics. At this level, there are courses with the generic name of Structure of Matter dealing with Lorentz transformations and the basic concepts of quantum mechanics. My course aimed at the same level. Its main constraint was that it had to be taught as a one-semester course, so that it would be accepted in physics and astronomy curricula.
The present book is based on that course, given three times to physics and astronomy students in Helsinki. Of course there already exist good books on cosmology. The reader will in fact find many references to such books, which have been an invaluable source of information to me. The problem is only that they address a postgraduate audience that intends to specialize in cosmology research.
My readers will have to turn to these books later when they have mastered all the professional skills of physics and mathematics. In this book I am not attempting to teach basic physics to astronomers. They will need much more. I am trying to teach just enough physics to be able to explain the main ideas in cosmology without too much hand-waving.
I have tried to avoid the other extreme, practised by some of my particle physics colleagues, of writing books on cosmology with the obvious intent of making particle physicists out of every theoretical astronomer. Introduction to Cosmology Third Edition by Matts Roos © 2003 John Wiley & Sons, Ltd ISBN 0 470 84909 6 (cased) ISBN 0 470 84910 X (pbk) www.com x Preface to First Edition I also do not attempt to teach basic astronomy to physicists. In contrast to astronomy scholars, I think the main ideas in cosmology do not require very detailed knowledge of astrophysics or observational techniques. Whole books have been written on distance measurements and the value of the Hubble param- eter, which still remains imprecise to a factor of two.
Physicists only need to know that quantities entering formulae are measurable—albeit incorporating factors h to some power—so that the laws can be discussed meaningfully. At undergraduate level, it is not even usual to give the errors on measured values. In most chapters there are subjects demanding such a mastery of theoretical physics or astrophysics that the explanations have to be qualitative and the deriva- tions meagre, for instance in general relativity, spontaneous symmetry breaking, inflation and galaxy formation. This is unavoidable because it just reflects the level of undergraduates.
My intention is to go just a few steps further in these matters than do the popular monographs. I am indebted in particular to two colleagues and friends who offered construc- tive criticism and made useful suggestions. The particle physicist Professor Kari Enqvist of NORDITA, Copenhagen, my former student, has gone to the trouble of reading the whole manuscript. The space astronomer Professor Stuart Bowyer of the University of California, Berkeley, has passed several early mornings of jet lag in Lapland going through the astronomy-related sections.
Anyway, he could not go out skiing then because it was either a snow storm or −30 ◦ C! Finally, the publisher provided me with a very knowledgeable and thorough referee, an astro- physicist no doubt, whose criticism of the chapter on galaxy formation was very valuable to me. For all remaining mistakes I take full responsibility. They may well have been introduced by me afterwards. Thanks are also due to friends among the local experts: particle physicist Pro- fessor Masud Chaichian and astronomer Professor Kalevi Mattila have helped me with details and have answered my questions on several occasions.
I am also indebted to several people who helped me to assemble the pictorial material: Drs Subir Sarkar in Oxford, Rocky Kolb in the Fermilab, Carlos Frenk in Durham, Werner Kienzle at CERN and members of the COBE team. Finally, I must thank my wife Jacqueline for putting up with almost two years of near absence and full absent-mindedness while writing this book. Matts Roos www.com Preface to Second Edition In the three years since the first edition of this book was finalized, the field of cosmology has seen many important developments, mainly due to new obser- vations with superior instruments such as the Hubble Space Telescope and the ground-based Keck telescope and many others. Thus a second edition has become necessary in order to provide students and other readers with a useful and up-to- date textbook and reference book.
At the same time I could balance the presentation with material which was not adequately covered before—there I am in debt to many readers. Also, the inevitable number of misprints, errors and unclear formulations, typical of a first edition, could be corrected. I am especially indebted to Kimmo Kainulainen who served as my course assistant one semester, and who worked through the book and the problems thoroughly, resulting in a very long list of corrigenda. A similar shorter list was also dressed by George Smoot and a student of his.
It still worries me that the errors found by George had been found neither by Kimmo nor by myself, thus statistics tells me that some errors still will remain undetected. For new pictorial material I am indebted to Wes Colley at Princeton, Carlos Frenk in Durham, Charles Lineweaver in Strasbourg, Jukka Nevalainen in Helsinki, Subir Sarkar in Oxford, and George Smoot in Berkeley. I am thankful to the Academie des Sciences for an invitation to Paris where I could visit the Observatory of Paris- Meudon and profit from discussions with S. Bonazzola and Brandon Carter.
Several of my students have contributed in various ways: by misunderstandings, indicating the need for better explanations, by their enthusiasm for the subject, and by technical help, in particular S. Harun-or-Rashid. My youngest grandchild Adrian (not yet 3) has showed a vivid interest for supernova bangs, as demon- strated by an X-ray image of the Cassiopeia A remnant. Thus the future of the subject is bright.
Matts Roos Introduction to Cosmology Third Edition by Matts Roos © 2003 John Wiley & Sons, Ltd ISBN 0 470 84909 6 (cased) ISBN 0 470 84910 X (pbk) www.com Preface to Third Edition This preface can start just like the previous one: in the seven years since the second edition was finalized, the field of cosmology has seen many important developments, mainly due to new observations with superior instruments.