Cosmology, by Steven Weinberg

Cosmology Steven Weinberg University of Texas at Austin 1 3 Great Clarendon Street, Oxford OX2 6DP Oxford University Press is a department of the University of Oxford. It furthers the University’s objective of excellence in research, scholarship, and education by publishing worldwide in Oxford New York Auckland Cape Town Dar es Salaam Hong Kong Karachi Kuala Lumpur Madrid Melbourne Mexico City Nairobi New Delhi Shanghai Taipei Toronto With offices in Argentina Austria Brazil Chile Czech Republic France Greece Guatemala Hungary Italy Japan Poland Portugal Singapore South Korea Switzerland Thailand Turkey Ukraine Vietnam Oxford is a registered trade mark of Oxford University Press in the UK and in certain other countries Published in the United States by Oxford University Press Inc., New York © Steven Weinberg 2008 The moral rights of the author have been asserted Database right Oxford University Press (maker) © First published 2008 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, without the prior permission in writing of Oxford University Press, or as expressly permitted by law, or under terms agreed with the appropriate reprographics rights organization. Enquiries concerning reproduction outside the scope of the above should be sent to the Rights Department, Oxford University Press, at the address above You must not circulate this book in any other binding or cover and you must impose the same condition on any acquirer British Library Cataloguing in Publication Data Data available Library of Congress Cataloging in Publication Data Data available Typeset by Newgen Imaging Systems (P) Ltd., Chennai, India Printed in Great Britain on acid-free paper by Biddles Ltd., King’s Lynn, Norfolk ISBN 978–0–19–852682–7 10987654321 To Louise, Elizabeth, and Gabrielle This page intentionally left blank Preface Research in cosmology has become extraordinarily lively in the past quarter century. In the early 1980s the proposal of the theory of inflation offered a solution to some outstanding cosmological puzzles and provided a mechanism for the origin of large-scale structure, which could be tested by observations of anisotropies in the cosmic microwave background. November 1989 saw the launch of the Cosmic Background Explorer Satellite. Measurements with its spectrophotometer soon established the thermal nature of the cosmic microwave background and determined its temperature to three decimal places, a precision unprecedented in cosmology. A little later the long-sought microwave background anisotropies were found in data taken by the satellite’s radiometer. Subsequent observations by ground-based and balloon-borne instruments and eventually by the Wilkinson Microwave Anisotropy Probe showed that these anisotropies are pretty much what would be expected on the basis of inflationary theory. In the late 1990s the use of Type Ia supernovae as standard candles led to the discovery that the expansion of the universe is accelerating, implying that most of the energy of the universe is some sort of dark energy, with a ratio of pressure to density less than −1/3. This was confirmed by precise observations of the microwave background anisotropies, and by massive surveys of galaxies, which together provided increasingly accurate values for cosmological parameters. Meanwhile, the classic methods of astronomy have provided steadily improving independent constraints on the same cosmological parameters. The spectroscopic discovery of thorium and then uranium in the atmo- spheres of old stars, together with continued study of the turn-off from the main sequence in globular clusters, has narrowed estimates of the age of the universe. The measurement of the deuterium to hydrogen ratio in interstel- lar absorption combined with calculations of cosmological nucleosynthesis has given a good value for the cosmic density of ordinary baryonic matter, and shown that it is only about a fifth of the density of some sort of mysterious non-baryonic cold dark matter. Observations with the Hubble Space Telescope as well as ground-based telescopes have given increasingly precise values for the Hubble constant. It is greatly reassuring that some of the parameters measured by these other means have values consistent with those found in studies of the cosmic microwave background and large scale structure. Progress continues. In the years to come, we can expect definite information about whether the dark energy density is constant or evolv- ing, and we hope for signs of gravitational radiation that would open the v Preface era of inflation to observation. We may discover the nature of dark matter, either by artificially producing dark matter particles at new large accelerators, or by direct observation of natural dark matter particles imping- ing on the earth. It remains to be seen if in our times fundamental physical theory can provide a specific theory of inflation or explain dark matter or dark energy. This new excitement in cosmology came as if on cue for elementary particle physicists. By the 1980s the Standard Model of elementary particles and fields had become well established. Although significant theoretical and experimental work continued, there was now little contact between experiment and new theoretical ideas, and without this contact, particle physics lost much of its liveliness. Cosmology now offered the excitement that particle physicists had experienced in the 1960s and 1970s. In 1999 I finished my three-volume book on the quantum theory of fields (cited here as “QTF”), and with unaccustomed time on my hands, I set myself the task of learning in detail the theory underlying the great progress in cosmology made in the previous two decades. Although I had done some research on cosmology in the past, getting up to date now turned out to take a fair amount of work. Review articles on cosmology gave good summaries of the data, but they often quoted formulas without giving the derivation, and sometimes even without giving a reference to the original derivation. Occasionally the formulas were wrong, and therefore extremely difficult for me to rederive. Where I could find the original references, the articles sometimes had gaps in their arguments, or relied on hidden assumptions, or used unexplained notation. Often massive computer programs had taken the place of analytic studies. In many cases I found that it was easiest to work out the relevant theory for myself. This book is the result. Its aim is to give self-contained explanations of the ideas and formulas that are used and tested in modern cosmological observations. The book divides into two parts, each of which in my exp- erience teaching the subject provides enough material for a one-semester graduate course. The first part, Chapters 1 through 4, deals chiefly with the isotropic and homogeneous average universe, with only a brief introduction to the anisotropies in the microwave background in Section 2.6. These chapters are more-or-less in reverse chronological order; Chapter 1 concentrates on the universe since the formation of galaxies, corresponding roughly to redshifts z < 10; Chapter 2 deals with the microwave background, emit- ted at a redshift z 1, 000; Chapter 3 describes the early universe, from the beginning of the radiation-dominated expansion to a redshift z ≈ 104 when the density of radiation fell below that of matter; and Chapter 4 takes up the period of inflation that is believed to have preceded the radiation- dominated era. The second part, Chapters 5 through 10, concentrates on the departures from the average universe. After some general formalism vi Preface in Chapter 5 and its application to the evolution of inhomogeneities in Chapter 6, I return in Chapter 7 to the microwave background anisotropies, and take up the large scale structure of matter in Chapter 8. Gravitational lensing is discussed late, in Chapter 9, because its most important cosmological application may be in the use of weak lensing to study large scale structure. The treatment of inflation in Chapter 4 deals only with the average properties of the universe in the inflationary era; I return to inflation in Chapter 10, which discusses the growth of inhomogeneities from quantum fluctuations during inflation. To the greatest extent possible, I have tried throughout this book to present analytic calculations of cosmological phenomena, and not just report results obtained elsewhere by numerical computation. The calculations that are used in the literature to compare observation with theory necessarily take many details into account, which either make an analytic treatment impossible, or obscure the main physical features of the calculation. Where this is the case, I have not hesitated to sacrifice some degree of accuracy for greater transparency. This is especially the case in the hydrodynam- ical treatment of cosmic fluctuations in Sections 6.2 through 6.5, and in the treatment of large scale structure in Chapter 8. But in Section 6.1 and Appendix H I also give an account of the more accurate kinetic theory on which the modern cosmological computer codes are based. Both approaches are applied to the cosmic microwave background anisotropies in Chapter 7. So much has happened in cosmology since the 1960s that this book necessarily bears little resemblance to my 1972 treatise, Gravitation and Cosmology. On occasion I refer back to that book (cited here as “G&C”) for material that does not seem worth repeating here. Classical general relativity has not changed much since 1972 (apart from a great strengthen- ing of its experimental verification) so it did not seem necessary to cover gravitation as well as cosmology in the present book. However, as a conve- nience to readers who want to refresh their knowledge of general relativity, and to establish my notation, I provide a brief introduction to general relativity in Appendix B. Other appendices deal with technical material that is needed here and there in the book.

Load more