Introduction to Cosmology - Sharif

1 Introduction to Cosmology Third Edition Matts Roos Introduction to Cosmology Third Edition Introduction to Cosmology Third Edition Matts Roos 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): Visit our Home Page on or 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.

2 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 or faxed to (+44) 1243 770571. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the Publisher is not engaged in rendering professional services. If professional advice or other expert assis- tance is required, the services of a competent professional should be sought. Other Wiley Editorial O ces John Wiley & Sons Inc., 111 River Street, Hoboken, NJ 07030, USA. Jossey-Bass, 989 Market Street, San Francisco, CA 94103-1741, USA.

3 Wiley-VCH Verlag GmbH, Boschstr. 12, D-69469 Weinheim, Germany John Wiley & Sons Australia Ltd, 33 Park Road, Milton, Queensland 4064, Australia John Wiley & Sons (Asia) Pte Ltd, 2 Clementi Loop #02-01, Jin Xing Distripark, Singapore 129809. John Wiley & Sons Canada Ltd, 22 Worcester Road, Etobicoke, Ontario, Canada M9W 1L1. Wiley also publishes its books in a variety of electronic formats. 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. 3rd ed. p. cm. Includes bibliographical references and index. ISBN 0-470-84909-6 (acid-free paper) ISBN 0-470-84910-X (pbk. : acid-free paper).

4 1. Cosmology . I. Title. 2003. 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 Lucida Bright by T&T Productions Ltd, London. Printed and bound in Great Britain by Antony Rowe Ltd., Chippenham, Wilts. 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. 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 Markuntyt r (2002).

5 Contents Preface to First Edition ix Preface to Second Edition xi Preface to Third Edition xiii 1 From Newton to Hubble 1. Historical Cosmology 2. Inertial Frames and the Cosmological Principle 7. Olbers' Paradox 9. Hubble's Law 12. The Age of the Universe 17. Expansion in a Newtonian World 19. 2 Relativity 25. Lorentz Transformations and Special Relativity 25. Metrics of Curved Space-time 30. Relativistic Distance Measures 37. General Relativity and the Principle of Covariance 45. The Principle of Equivalence 49. Einstein's Theory of Gravitation 54. 3 Gravitational Phenomena 61. Classical Tests of General Relativity 62. The Binary Pulsar 63. Gravitational Lensing 64. Black Holes 71. Gravitational Waves 80.

6 4 Cosmological Models 87. Friedmann Lema tre Cosmologies 87. de Sitter Cosmology 99. Dark Energy 101. 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). viii Contents 5 Thermal History of the Universe 113. Photons 114. Adiabatic Expansion 117. Electroweak Interactions 122. The Early Radiation Era 128. Photon and Lepton Decoupling 132. Big Bang Nucleosynthesis 139. 6 Particles and Symmetries 149. Spin Space 150. SU(2) Symmetries 156. Hadrons and Quarks 159. The Discrete Symmetries C, P, T 163. Spontaneous Symmetry Breaking 166. Primeval Phase Transitions and Symmetries 171.

7 Baryosynthesis and Antimatter Generation 178. 7 Cosmic In ation 185. Paradoxes of the Expansion 186. Old' and New' In ation 192. Chaotic In ation 196. The In aton as Quintessence 202. Cyclic Models 205. 8 Cosmic Microwave Background 211. The CMB Temperature 212. Temperature Anisotropies 216. Polarization Anisotropies 222. Model Testing and Parameter Estimation. II 225. 9 Cosmic Structures and Dark Matter 231. Density Fluctuations 232. Structure Formation 237. The Evidence for Dark Matter 241. Dark Matter Candidates 248. The Cold Dark Matter Paradigm 252. 10 Epilogue 259. Singularities 259. Open Questions 262. Tables 267. Index 271. Preface to First Edition A few decades ago, astronomy and particle physics started to merge in the com- mon eld of Cosmology .

8 The general public had always been more interested in the visible objects of astronomy than in invisible atoms, and probably met cosmol- ogy rst 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.

9 At the University of Helsinki I decided to try to take advantage of the great interest in Cosmology among the younger students, o ering 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.

10 Of course there already exist good books on Cosmology . The reader will in fact nd 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.