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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 cs books wiley co uk. Visit our Home Page on www wileyeurope com or www wiley 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. 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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 . 1 Cosmology I Title ,QB981 R653 2003,523 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 5 12 5pt 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 . Contents,Preface to First Edition ix,Preface to Second Edition xi. Preface to Third Edition xiii,1 From Newton to Hubble 1. 1 1 Historical Cosmology 2, 1 2 Inertial Frames and the Cosmological Principle 7. 1 3 Olbers Paradox 9, 1 4 Hubble s Law 12, 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 3 Gravitational Lensing 64. 3 4 Black Holes 71, 3 5 Gravitational Waves 80,4 Cosmological Models 87. 4 1 Friedmann Lema tre Cosmologies 87, 4 2 de Sitter Cosmology 99. 4 3 Dark Energy 101, 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 . viii Contents,5 Thermal History of the Universe 113. 5 1 Photons 114, 5 2 Adiabatic Expansion 117, 5 3 Electroweak Interactions 122. 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 1 Spin Space 150, 6 2 SU 2 Symmetries 156, 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 In ation 185. 7 1 Paradoxes of the Expansion 186, 7 2 Old and New In ation 192. 7 3 Chaotic In ation 196, 7 4 The In aton as Quintessence 202. 7 5 Cyclic Models 205,8 Cosmic Microwave Background 211. 8 1 The CMB Temperature 212, 8 2 Temperature Anisotropies 216. 8 3 Polarization Anisotropies 222, 8 4 Model Testing and Parameter Estimation II 225. 9 Cosmic Structures and Dark Matter 231, 9 1 Density Fluctuations 232. 9 2 Structure Formation 237, 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 1 Singularities 259, 10 2 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 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 , 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 . 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 , 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 . 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 . in ation and galaxy formation This is unavoidable because it just re ects 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 o ered 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, Preface to Second Edition, In the three years since the rst edition of this book was nalized the eld 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 rst. 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 pro t 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 M 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 . Preface to Third Edition, This preface can start just like the previous one in the seven years since the. second edition was nalized the eld of cosmology has seen many important. developments mainly due to new observations with superior instruments In the. past cosmology often relied on philosophical or aesthetic arguments now it is. maturing to become an exact science For example the Einstein de Sitter universe . which has zero cosmological constant 0 used to be favoured for esthetical. reasons but today it is known to be very di erent from zero 0 73 0 04 . In the rst edition I quoted 0 0 8 0 3 daring to believe in errors that many. others did not which gave room for all possible spatial geometries spherical at. and hyperbolic Since then the value has converged to 0 1 02 0 02 and every . body is now willing to concede that the geometry of the Universe is at 0 1 . This result is one of the cornerstones of what we now can call the Standard Model. of Cosmology Still deep problems remain so deep that even Einstein s general. relativity is occasionally put in doubt , A consequence of the successful march towards a standard model is that many. alternative models can be discarded An introductory text of limited length like. the current one cannot be a historical record of failed models Thus I no longer. discuss or discuss only brie y k 0 geometries the Einstein de Sitter universe . hot and warm dark matter cold dark matter models with 0 isocurvature uc . tuations topological defects except monopoles Bianchi universes and formulae. which only work in discarded or idealized models like Mattig s relation and the. Saha equation , Instead this edition contains many new or considerably expanded subjects Sec . tion 2 3 on Relativistic Distance Measures Section 3 3 on Gravitational Lensing . Section 3 5 on Gravitational Waves Section 4 3 on Dark Energy and Quintessence . Section 5 1 on Photon Polarization Section 7 4 on The In aton as Quintessence . Section 7 5 on Cyclic Models Section 8 3 on CMB Polarization Anisotropies Sec . tion 8 4 on model testing and parameter estimation using mainly the rst year. CMB results of the Wilkinson Microwave Anisotropy Probe and Section 9 5 on. large scale structure results from the 2 degree Field 2dF Galaxy Redshift Survey . The synopsis in this edition is also di erent and hopefully more logical much has. been entirely rewritten and all parameter values have been updated . I have not wanted to go into pure astrophysics but the line between cosmology. and cosmologically important astrophysics is not easy to draw Supernova explo . sion mechanisms and black holes are included as in the earlier editions but not. 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 . xiv Preface to Third Edition, for instance active galactic nuclei AGNs or jets or ultra high energy cosmic rays . Observational techniques are mentioned only brie y they are beyond the scope. of this book , There are many new gures for which I am in debt to colleagues and friends . all acknowledged in the gure legends I have pro ted from discussions with Pro . fessor Carlos Frenk at the University of Durham and Professor Kari Enqvist at. the University of Helsinki I am also indebted to Professor Juhani Keinonen at the. University of Helsinki for having generously provided me with working space and. access to all the facilities at the Department of Physical Sciences despite the fact. that I am retired , Many critics referees and other readers have made useful comments that I have. tried to take into account One careful reader Urbana Lopes Fran a Jr sent me. a long list of misprints and errors A critic of the second edition stated that the. errors in the rst edition had been corrected but that new errors had emerged. in the new text This will unfortunately always be true in any comparison of edi . tion n 1 with edition n In an attempt to make continuous corrections I have. assigned a web site for a list of errors and misprints The address is. http www physics helsinki cosmo , My most valuable collaborator has been Thomas S Coleman a nonphysicist who. contacted me after having spotted some errors in the second edition and who. proposed some improvements in case I were writing a third edition This came. at the appropriate time and led to a collaboration in which Thomas S Coleman. read the whole manuscript corrected misprints improved my English checked. my calculations designed new gures and proposed clari cations where he found. the text di cult , My wife Jacqueline has many interesting subjects of conversation at the break . fast table Regretfully her breakfast companion is absent minded thinking only. of cosmology I thank her heartily for her kind patience promising improvement . Matts Roos, Helsinki March 2003, 1, From Newton to. Hubble, The history of ideas on the structure and origin of the Universe shows that. humankind has always put itself at the centre of creation As astronomical evi . dence has accumulated these anthropocentric convictions have had to be aban . doned one by one From the natural idea that the solid Earth is at rest and the. celestial objects all rotate around us we have come to understand that we inhabit. an average sized planet orbiting an average sized sun that the Solar System is in. the periphery of a rotating galaxy of average size ying at hundreds of kilometres. per second towards an unknown goal in an immense Universe containing billions. of similar galaxies , Cosmology aims to explain the origin and evolution of the entire contents of. the Universe the underlying physical processes and thereby to obtain a deeper. understanding of the laws of physics assumed to hold throughout the Universe . Unfortunately we have only one universe to study the one we live in and we. cannot make experiments with it only observations This puts serious limits on. what we can learn about the origin If there are other universes we will never know . Although the history of cosmology is long and fascinating we shall not trace it. in detail nor any further back than Newton accounting in Section 1 1 only for. those ideas which have fertilized modern cosmology directly or which happened. to be right although they failed to earn timely recognition In the early days of. cosmology when little was known about the Universe the eld was really just a. branch of philosophy , Having a rigid Earth to stand on is a very valuable asset How can we describe. motion except in relation to a xed point Important understanding has come. from the study of inertial systems in uniform motion with respect to one another . From the work of Einstein on inertial systems the theory of special relativity. 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 . 2 From Newton to Hubble, was born In Section 1 2 we discuss inertial frames and see how expansion and. contraction are natural consequences of the homogeneity and isotropy of the. Universe , A classic problem is why the night sky is dark and not blazing like the disc of. the Sun as simple theory in the past would have it In Section 1 3 we shall discuss. this so called Olbers paradox and the modern understanding of it . The beginning of modern cosmology may be xed at the publication in 1929. of Hubble s law which was based on observations of the redshift of spectral. lines from remote galaxies This was subsequently interpreted as evidence for. the expansion of the Universe thus ruling out a static Universe and thereby set . ting the primary requirement on theory This will be explained in Section 1 4 In. Section 1 5 we turn to determinations of cosmic timescales and the implications. of Hubble s law for our knowledge of the age of the Universe . In Section 1 6 we describe Newton s theory of gravitation which is the earliest. explanation of a gravitational force We shall modernize it by introducing Hub . ble s law into it In fact we shall see that this leads to a cosmology which already. contains many features of current Big Bang cosmologies . 1 1 Historical Cosmology, At the time of Isaac Newton 1642 1727 the heliocentric Universe of Nicolaus. Copernicus 1473 1543 Galileo Galilei 1564 1642 and Johannes Kepler 1571 . 1630 had been accepted because no sensible description of the motion of the. planets could be found if the Earth was at rest at the centre of the Solar System . Humankind was thus dethroned to live on an average sized planet orbiting around. an average sized sun , The stars were understood to be suns like ours with xed positions in a static. Universe The Milky Way had been resolved into an accumulation of faint stars. with the telescope of Galileo The anthropocentric view still persisted however . in locating the Solar System at the centre of the Universe . Newton s Cosmology The rst theory of gravitation appeared when Newton. published his Philosophiae Naturalis Principia Mathematica in 1687 With this. theory he could explain the empirical laws of Kepler that the planets moved in. elliptical orbits with the Sun at one of the focal points An early success of this. theory came when Edmund Halley 1656 1742 successfully predicted that the. comet sighted in 1456 1531 1607 and 1682 would return in 1758 Actually the. rst observation con rming the heliocentric theory came in 1727 when James. Bradley 1693 1762 discovered the aberration of starlight and explained it as. due to the changes in the velocity of the Earth in its annual orbit In our time . Newton s theory of gravitation still su ces to describe most of planetary and. satellite mechanics and it constitutes the nonrelativistic limit of Einstein s rela .
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