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Steven Weinberg The First Three Minutes A modem view of the origin of the universe FLAMINGO Published by Fontana Paperbacks

Contents Preface 9 1 Introduction: the Giant and the Cow 13 2 The Expansion of the Universe 20 3 The Cosmic Microwave Radiation Background 52 4 Recipe for a Hot Universe 81 5 The First Three Minutes 102 6 A Historical Diversion 120 7 The First One-hundredth Second 130 8 Epilogue: the Prospect Ahead 145 Afterword 151 TABLES : 1. Properties of Some Elementary Particles 163 2. Properties of Some Kinds of Radiation 164 Glossary 165

Preface This book grew out of a talk I gave at the dedication of the Undergraduate Science Center at Harvard in November 1973. Erwin Glikes, president and publisher of Basic Books, heard of this talk from a mutual friend, Daniel Bell, and urged me to turn it into a book. At first I was not enthusiastic about the idea. Although I have done small bits of research in cosmology from time to time, my work has been much more concerned with the physics of the very small, the theory of elementary particles. Also, elementary particle physics has been extraordinarily lively in the last few years, and I had been spending too much time away from it, writing non-technical articles for various magazines. I wanted very much to return full time to my natural habitat, the Physical Review. However, I found that I could not stop thinking about the idea of a book on the early universe. What could be more interesting than the problem of Genesis? Also, it is in the early universe, especially the first hundredth of a second, that the problems of the theory of elementary particles come together with the problems of cosmology. Above all, this is a good time to write about the early universe. In just the last decade a detailed theory of the course of events in the early universe has become widely accepted as a 'standard model'. It is a remarkable thing to be able to say just what the universe was like at the end of the first second or the first minute or the first year. To a physicist, the exhilarating thing is to be able to work things out numerically, to be able to say that at such and such a time the temperature and density and chemical composition of the universe had such

10 The First Three Minutes and such values. True, we are not absolutely certain about all this, but it is exciting that we are now able to speak of such things with any confidence at all. It was this excitement that I wanted to convey to the reader. I had better say for what reader this book is intended. I have written for one who is willing to puzzle through some detailed arguments, but who is not at home in either mathe- matics or physics. Although I must introduce some fairly complicated scientific ideas, no mathematics is used in the body of the book beyond arithmetic, and little or no knowl- edge of physics or astronomy is assumed in advance. I have tried to be careful to define scientific terms when they are first used, and in addition I have supplied a glossary of physical and astronomical terms (p. 165). Wherever possible, I have also written numbers like 'a hundred thousand million' in English, rather than use the more convenient scientific notation: 1011. However, this does not mean that I have tried to write an easy book. When a lawyer writes for the general public, he assumes that they do not know Law French or the Rule Against Perpetuities, but he does not think the worse of them for it, and he does not condescend to them. I want to return the compliment: I picture the reader as a smart old attorney who does not speak my language, but who expects nonethe- less to hear some convincing arguments before he makes up his mind. For the reader who does want to see some of the calcula- tions that underlie the arguments of this book, I have pre- pared 'A Mathematical Supplement', which follows the body of the book (p. 175). The level of mathematics used here would make these notes accessible to anyone with an under- graduate concentration in any physical science or mathe- matics. Fortunately, important calculations in cosmology are rather simple; it is only here and there that the finer points of general relativity or nuclear physics come into play. Readers who want to pursue this subject on a more technical level will find several advanced treatises the most

Preface 11 (including my own) listed under 'Suggestions for Further Reading' (p. 189). I should also make clear what subject I intended this book to cover. It is definitely not a book about all aspects of cosmology. There is a 'classic' part of the subject, which has to do mostly with the large-scale structure of the present universe: the debate over the extragalactic nature of the spiral nebulae; the discovery of the red shifts of distant galaxies and their dependence on distance; the general relativ- istic cosmological models of Einstein, de Sitter, Lemaitre, and Friedmann; and so on. This part of cosmology has been described very well in a number of distinguished books, and I did not intend to give another full account of it here. The present book is concerned with the early universe, and in particular with the new understanding of the early universe that has grown out of the discovery of the cosmic microwave radiation background in 1965. Of course, the theory of the expansion of the universe is an essential ingredient in our present view of the early uni- verse, so I have been compelled in Chapter 2 to provide a brief introduction to the more 'classic' aspects of cosmology. I believe that this chapter should provide an adequate back- ground, even for the reader completely unfamiliar with cosmology, to understand the recent developments in the theory of the early universe with which the rest of the book is concerned. However, the reader who wants a thorough introduction to the older parts of cosmology is urged to consult the books listed under 'Suggestions for Further Reading'. On the other hand, I have not been able to find any coherent historical account of the recent developments in cosmology. I have therefore been obliged to do a little digging myself, particularly with regard to the fascinating question of why there was no search for the cosmic microwave radia- tion background long before 1965. (This is discussed in Chapter 6.) This is not to say that I regard this book as a definitive history of these developments - I have far too much

12 The First Three Minutes respect for the effort and attention to detail needed in the history of science to have any illusions on that score. Rather, I would be happy if a real historian of science would use this book as a starting point, and write an adequate history of the last thirty years of cosmological research. I am extremely grateful to Erwin Glikes and Farrell Phillips of Basic Books for their valuable suggestions in preparing this manuscript for publication. I have also been helped more than I can say in writing this book by the kind advice of my colleagues in physics and astronomy. For taking the trouble to read and comment on portions of the book, I wish especially to thank" Ralph Alpher, Bernard Burke, Robert Dicke, George Field, Gary Feinberg, William Fowler, Robert Herman, Fred Hoyle, Jim Peebles, Arno Penzias, Bill Press, Ed Purcell and Robert Wagoner. My thanks are also due to Isaac Asimov, I. Bernard Cohen, Martha Liller and Philip Morrison for information on various special-topics. I am particularly grateful to Nigel Calder for reading through the whole of the first draft, and for his perceptive comments. I cannot hope that this book is now entirely free of errors and obscurities, but I am certain that it is a good deal clearer and more accurate than it could have been without all the generous assistance I have been fortunate enough to receive. Cambridge, Massachusetts July 1976 S T E V EN W E I N B E RG

Introduction: the Giant and the Cow The origin of the universe is explained in the Younger Edda, a collection of Norse myths compiled around 1220 by the Icelandic magnate Snorri Sturleson. In the beginning, says the Edda, there was nothing at all. 'Earth was not found, nor Heaven above, a Yawning-gap there was, but grass nowhere.' To the north and south of nothing lay regions of frost and fire, Niflheim and Muspelheim. The heat from Muspelheim melted some of the frost from Niflheim, and from the liquid drops there grew a giant, Ymer. What did Ymer eat? It seems there was also a cow, Audhumla. And what did she eat? Well, there was also some salt. And so on. I must not offend religious sensibilities, even Viking reli- gious sensibilities, but I think it is fair to say that this is not a very satisfying picture of the origin of the universe. Even leaving aside all objections to hearsay evidence, the story raises as many problems as it answers, and each answer requires a new complication in the initial conditions. We are not able merely to smile at the Edda, and forswear all cosmogonical speculation - the urge to trace the history of the universe back to its beginning is irresistible. From the start of modem science in the sixteenth and seventeenth centuries, physicists and astronomers have returned again and again to the problem of the origin of the universe. However, an aura of the disreputable always surrounded such research. I remember that during the time that I was a student and then began my own research (on other problems) in the 1950s, the study of the early universe was widely regarded as not the sort of thing to which a respectable scientist would devote his time. Nor was this Judgement

14 The First Three Minutes unreasonable. Throughout most of the history of modem physics and astronomy, there simply has not existed an adequate observational and theoretical foundation on which to build a history of the early universe. Now, in just the past decade, all this has changed. A theory of the early universe has become so widely accepted that astronomers often call it 'the standard model'. It is more or less the same as what is sometimes called the 'big bang' theory, but supplemented with a much more specific recipe for the contents of the universe. This theory of the early universe is the subject of this book. To help see where we are going, it may be useful to start with a summary of the history of the early universe, as presently understood in the standard model. This is only a brief run-through - succeeding chapters will explain the details of this history, and our reasons for believing any of it. In the beginning there was an explosion. Not an explosion like those familiar on earth, starting from a definite centre and spreading out to engulf more and more of the circum- ambient air, but an explosion which occurred simultaneously everywhere, filling all space from the beginning, with every particle of matter rushing apart from every other particle. 'All space' in this context may mean either all of an infinite universe, or all of a finite universe which curves back on itself like the surface of a sphere. Neither possibility is easy to comprehend, but this will not get in our way; it matters hardly at all in the early universe whether space is finite or infinite. At about one-hundredth of a second, the earliest time about which we can speak with any confidence, the temperature of the universe was about a hundred thousand million (1011) degrees Centigrade. This is much hotter than in the centre of even the hottest star, so hot, in fact, that none of the components of ordinary matter, molecules, or atoms, or even the nuclei of atoms, could have held together. Instead, the matter rushing apart in this explosion consisted of various

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