DMITRY S GORBUNOV s VALERY A RUBAKOV INTRODUCTION TO THE THEORY OF THE EARLY UNIVERSE Hot Big Bang Theory INTRODUCTION TO THE THEORY 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 THE THEORY OF THE EARLY UNIVERSE Hot Big Bang Theory :RUOG6FLHQWLÀF NEW J E R S E Y t L O N D O N t S I N G A P O R E t B E I J I N G t S H A N G H A I t H O N G K O N G t TA I P E I t C H E N N A I 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: To Olesya and Elvira This page is intentionally left blank Preface It is clear by now that there is deep interconnection between cosmology and particle physics, between macro- and micro-worlds. This book is written precisely from this perspective. We present here the results on the homogeneous and isotropic Universe at the hot stage of its evolution and at subsequent stages. This part of cosmology is often dubbed as the Hot Big Bang theory. In the accompanying book we study the theory of cosmological perturbations (inhomogeneities in the Universe), 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 Lomonosov Moscow State University. This course is aimed at under- graduate students specializing in theoretical physics. We decided, however, to add a 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 have not found their compelling solutions yet. Most of the additional material deals with hypotheses on these problems that at the moment compete with each other. Knowledge of material taught in general physics courses is in principle sufficient for reading the main Chapters of this book. So, the main Chapters must be under- standable by undergraduate students. The necessary material on General Relativity and particle physics is collected in Appendices which, of course, do not pretend to give comprehensive account of these areas of physics. On the other hand, some parts labeled by asterisks make use of the methods of classical and quantum field theory as well as nonequilibrium statistical mechanics, so basic knowledge of these methods 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 touch upon are considered in detail. Certainly, this list is by no means complete. 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. Observational and experimental data we quote, the results of their compilations 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 of the Russian Academy of Sciences F. 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–Walker Metric . . . . . . . . . . . 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