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DMITRY S GORBUNOV VALERY A RUBAKOV (cid:115) INTRODUCTION TO THEORY THE OF THE EARLY UNIVERSE Hot Big Bang Theory INTRODUCTION TO THEORY THE OF THE EARLY UNIVERSE Hot Big Bang Theory This page is intentionally left blank DMITRY S GORBUNOV Institute for Nuclear Research of the Russian Academy of Sciences VALERY A RUBAKOV Institute for Nuclear Research of the Russian Academy of Sciences & Moscow State University INTRODUCTION TO THEORY THE OF THE EARLY UNIVERSE Hot Big Bang Theory (cid:2)(cid:3)(cid:4)(cid:5)(cid:6)(cid:7)(cid:8)(cid:9)(cid:10)(cid:11)(cid:12)(cid:13)(cid:10)(cid:14)(cid:9) NEW JERSEY LONDON SINGAPORE BEIJING SHANGHAI HONG KONG TAIPEI CHENNAI (cid:116) (cid:116) (cid:116) (cid:116) (cid:116) (cid:116) (cid:116) Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library. INTRODUCTION TO THE THEORY OF THE EARLY UNIVERSE Hot Big Bang Theory Copyright © 2011 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN-13 978-981-4322-24-9 ISBN-10 981-4322-24-5 ISBN-13 978-981-4343-97-8 (pbk) ISBN-10 981-4343-97-8 (pbk) Typeset by Stallion Press Email: [email protected] Printed in Singapore. To Olesya and Elvira This page is intentionally left blank Preface Itisclearbynowthatthereisdeepinterconnectionbetweencosmologyandparticle physics, between macro-and micro-worlds.This book is written precisely fromthis perspective.WepresentheretheresultsonthehomogeneousandisotropicUniverse atthe hotstageofits evolutionandatsubsequentstages.Thispartofcosmologyis often dubbed as the Hot Big Bang theory. In the accompanyingbook we study the theoryofcosmologicalperturbations(inhomogeneitiesintheUniverse),inflationary theory and theory of post-inflationary reheating. This book grew from the lecture course which is being taught for a number of years at the Department of Quantum Statistics and Field Theory of the Physics Faculty of the LomonosovMoscowState University.This courseis aimed at under- graduatestudentsspecializingintheoreticalphysics.Wedecided,however,toadda number of more advanced Chapters and Sections which we mark by asterisks. The reason is that there are problems in cosmology (nature of dark matter and dark energy, mechanism of the matter-antimatter asymmetry generation, etc.) which havenotfoundtheircompellingsolutionsyet.Mostoftheadditionalmaterialdeals with hypotheses on these problems that at the moment compete with each other. Knowledgeofmaterialtaughtingeneralphysicscoursesis in principlesufficient for reading the main Chapters of this book. So, the main Chapters must be under- standablebyundergraduatestudents.ThenecessarymaterialonGeneralRelativity and particle physics is collected in Appendices which, of course, do not pretend to givecomprehensiveaccountoftheseareasofphysics.Ontheotherhand,someparts labeled by asterisks make use of the methods of classical and quantum field theory aswellasnonequilibriumstatisticalmechanics,sobasicknowledgeofthesemethods is required for reading these parts. Literature on cosmology is huge, and presenting systematic and comprehensive bibliography would be way out of the scope of this book. To orient the reader, in the end of this book we give a list of monographs and reviews where the issues we touchuponareconsideredindetail.Certainly,thislistisbynomeanscomplete.We occasionally refer to original literature, especially in those places where we present concrete results without detailed derivation. vii viii Preface Both observational cosmology and experimental particle physics develop very fast.Observationalandexperimentaldatawequote,theresultsoftheircompilations and fits (values of the cosmological parameters, limits on masses and couplings of hypothetical particles, etc.) will most probably get more precise even before this book is published. This drawback can be corrected, e.g., by using the regularly updated material of Particle Data Group at http://pdg.lbl.gov/. We would like to thank our colleagues from the Institute for Nuclear Research ofthe RussianAcademyofSciencesF. L.Bezrukov,S. V. Demidov, V. A. Kuzmin, D. G. Levkov, M. V. Libanov, E. Y. Nugaev, G. I. Rubtsov, D. V. Semikoz, P. G. Tinyakov, I. I. Tkachev and S. V. Troitsky for participation in the prepa- ration of the lecture course and numerous helpful discussions and comments. Our special thanks are to S. L. Dubovsky who participated in writing this book at an early stage. We are deeply indebted to V. S. Berezinsky, A. Boyarsky, A. D. Dolgov, D. I. Kazakov, S. Y. Khlebnikov, V. F. Mukhanov, I. D. Novikov, K.A.Postnov,M.V.Sazhin,M.E.Shaposhnikov,A.Y.Smirnov,A.A.Starobinsky, R.A.Sunyaev,A.N.Tavkhelidze,O.V.Verkhodanov,A.Vilenkin, M.B.Voloshin and M. I. Vysotsky for many useful comments and criticism. Contents Preface vii 1. Cosmology: A Preview 1 1.1 Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 The Universe Today . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 Homogeneity and isotropy . . . . . . . . . . . . . . . . . . 3 1.2.2 Expansion . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.3 Age of the Universe and size of its observable part . . . . . 7 1.2.4 Spatial flatness . . . . . . . . . . . . . . . . . . . . . . . . . 9 1.2.5 “Warm” Universe . . . . . . . . . . . . . . . . . . . . . . . 9 1.3 Energy Balance in the Present Universe . . . . . . . . . . . . . . . 13 1.4 Future of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . 19 1.5 Universe in the Past . . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.5.1 Recombination . . . . . . . . . . . . . . . . . . . . . . . . . 20 1.5.2 Big Bang Nucleosynthesis (BBN) . . . . . . . . . . . . . . 21 1.5.3 Neutrino decoupling . . . . . . . . . . . . . . . . . . . . . . 22 1.5.4 Cosmological phase transitions . . . . . . . . . . . . . . . . 23 1.5.5 Generation of baryon asymmetry . . . . . . . . . . . . . . 24 1.5.6 Generation of dark matter . . . . . . . . . . . . . . . . . . 25 1.6 Structure Formation in the Universe . . . . . . . . . . . . . . . . . 25 1.7 Inflationary Epoch . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 2. Homogeneous Isotropic Universe 29 2.1 Homogeneous Isotropic Spaces . . . . . . . . . . . . . . . . . . . . 29 2.2 Friedmann–Lemaˆıtre–Robertson–WalkerMetric . . . . . . . . . . . 32 2.3 Redshift. Hubble Law . . . . . . . . . . . . . . . . . . . . . . . . . 34 2.4 Slowing Down of Relative Motion . . . . . . . . . . . . . . . . . . . 38 2.5 Gases of Free Particles in Expanding Universe. . . . . . . . . . . . 40 3. Dynamics of Cosmological Expansion 45 3.1 Friedmann Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 45 ix