Table Of ContentDMITRY 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
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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
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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
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INTRODUCTION TO THE THEORY OF THE EARLY UNIVERSE
Hot Big Bang Theory
Copyright © 2011 by World Scientific Publishing Co. Pte. Ltd.
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ISBN-13 978-981-4322-24-9
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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
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