Intro 2 Particle Cosmology - The Standard Model of Cosmology

257 Pages·2016·2.82 MB·English

UNITEXT for Physics
Cosimo Bambi
Alexandre D. Dolgov
Introduction
to Particle
Cosmology
The Standard Model of Cosmology
and its Open Problems
UNITEXT for Physics
Series editors
Michele Cini, Roma, Italy
Attilio Ferrari, Torino, Italy
Stefano Forte, Milano, Italy
Guido Montagna, Pavia, Italy
Oreste Nicrosini, Pavia, Italy
Luca Peliti, Napoli, Italy
Alberto Rotondi, Pavia, Italy
Cosimo Bambi Alexandre D. Dolgov
(cid:129)
Introduction to Particle
Cosmology
The Standard Model of Cosmology
and its Open Problems
123
Cosimo Bambi Alexandre D.Dolgov
Department ofPhysics DipartimentodiFisicaeScienzedellaTerra
FudanUniversity Universitàdegli Studi diFerrara
Shanghai Ferrara
China Italy
and
Department ofPhysics
Novosibirsk State University
Novosibirsk
Russia
ISSN 2198-7882 ISSN 2198-7890 (electronic)
UNITEXTfor Physics
ISBN978-3-662-48077-9 ISBN978-3-662-48078-6 (eBook)
DOI 10.1007/978-3-662-48078-6
LibraryofCongressControlNumber:2015945603
SpringerHeidelbergNewYorkDordrechtLondon
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Preface
Overthepast20years,cosmologyhasemergedasamatureresearchfield,inwhich
it is possible to perform precise measurements and test fundamental physics. Its
significance in relation to the other areas of research in physics has grown sub-
stantially.Towit,twooutoftenNobelPrizesinphysicsawardedduringthepast10
years were conferred for studies related to cosmology (in 2006 and in 2011).
Among the preceding more than 100 awards, only one-half of one Nobel Prize (in
1978) was for cosmology.
The number of researchers working in cosmology is increasing, and students
takingintroductorycoursesoncosmologyincludenotonlythosewhoplantowork
in this field, but also those with different interests, seeking to get at least a basic
understanding of the subject.
The aim of this book is to provide an introduction to modern cosmology for
seniorundergraduateandgraduatephysicsstudents,withoutnecessarilyrequiringa
strong background in theoretical high energy physics. Students in
astronomy/astrophysics, in experimental high energy physics, or in other areas of
research as well may be interested to learn some fundamental concepts of the
structure and evolution of the Universe. Typically, these students are not closely
familiar with General Relativity and quantum field theory, and therefore they may
find it difficult to digest the existing cosmology books on the market.
This book describes the so-called Standard Cosmological Model. The model’s
theoretical aspects are based on General Relativity and on the Standard Model of
particle physics, with the addition of the inflationary paradigm. This scenario is
very successful in explaining a large amount of observational data including, in
particular, the description of the Universe expansion, the primordial abundances
of the light elements, and the origin and the properties of the cosmic microwave
background radiation. However, there is also a plethora of observed phenomena
thatdoesnotfittheframeworksoftheMinimalStandardModelofparticlephysics
and cosmology, and represents clear indications for new physics. To name just a
few examples, the minimal model cannot explain the cosmological matter-
antimatter asymmetry, the observed accelerated expansion of the contemporary
Universe, and does not have any candidate for dark matter. The cosmological
v
vi Preface
inflationisstillatthelevelofahypothesis.Itsrealizationdemandssomenewfield
or fields, which have not yet been discovered.
These subjects are presented here within a rather heuristic approach, which
includes a needed description of observational data, and a reduction of mathe-
matical technicalities as much as possible. Chapters 6 and 7, dealing, respectively,
withinflationandbaryogenesis,aremoreadvancedandrequiresomeknowledgeof
quantumfieldtheory,butstudentswhoarenotfamiliarwiththoseconceptscanskip
these chapters without affecting their comprehension of the rest of the book. The
content of this book is partially based on the cosmology class given at Fudan
University by one of the authors and on lectures given at a number of universities
by the other.
The work of C.B. was supported by the NSFC grant No. 11305038, the
Shanghai Municipal Education Commission grant No. 14ZZ001, the Thousand
YoungTalentsProgram,andFudanUniversity.TheworkofA.D.D.wassupported
by the grant of the Russian Federation Government 11.G34.31.0047.
Shanghai Cosimo Bambi
Novosibirsk Alexandre D. Dolgov
May 2015
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Problems in Newtonian Cosmology. . . . . . . . . . . . . . . . . . . . 2
1.2 The Standard Model of Cosmology. . . . . . . . . . . . . . . . . . . . 3
1.2.1 Hubble’s Law. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.2.2 Big Bang Nucleosynthesis. . . . . . . . . . . . . . . . . . . . 7
1.2.3 Cosmic Microwave Background. . . . . . . . . . . . . . . . 8
1.3 Evidence for New Physics. . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.3.1 Inflation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3.2 Baryogenesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.3 Dark Matter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.3.4 Cosmological Constant Problems . . . . . . . . . . . . . . . 13
1.4 Age and Size of the Universe. . . . . . . . . . . . . . . . . . . . . . . . 14
1.5 Cosmological Models Beyond General Relativity . . . . . . . . . . 16
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2 General Relativity. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.1 Scalars, Vectors and Tensors . . . . . . . . . . . . . . . . . . . . . . . . 17
2.2 Geodesic Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
2.2.1 Newtonian Mechanics. . . . . . . . . . . . . . . . . . . . . . . 20
2.2.2 Relativistic Mechanics. . . . . . . . . . . . . . . . . . . . . . . 21
2.3 Energy and Momentum in Flat Spacetime . . . . . . . . . . . . . . . 23
2.4 Energy-Momentum Tensor in Flat Spacetime. . . . . . . . . . . . . 24
2.5 Curved Spacetime. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.6 Field Theory in Flat and Curved Spacetimes . . . . . . . . . . . . . 27
2.7 Einstein Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
vii
viii Contents
3 The Standard Model of Particle Physics. . . . . . . . . . . . . . . . . . . . 35
3.1 Fermions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
3.1.1 Leptons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1.2 Quarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Bosons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.1 Gauge Bosons . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2.2 Higgs Particle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
3.3 Feynman Diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.4 Beyond the Minimal Standard Model of Particle Physics. . . . . 44
3.4.1 Supersymmetric Models. . . . . . . . . . . . . . . . . . . . . . 45
3.4.2 Grand Unification Theories . . . . . . . . . . . . . . . . . . . 46
3.4.3 Heavy Neutrinos. . . . . . . . . . . . . . . . . . . . . . . . . . . 48
3.4.4 Peccei-Quinn Model . . . . . . . . . . . . . . . . . . . . . . . . 49
3.5 Probabilities of Reactions Among Particles . . . . . . . . . . . . . . 49
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
4 Cosmological Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
4.1 Friedmann-Robertson-Walker Metric. . . . . . . . . . . . . . . . . . . 54
4.2 Friedmann Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
4.3 Cosmological Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
4.3.1 Einstein Universe . . . . . . . . . . . . . . . . . . . . . . . . . . 58
4.3.2 Matter Dominated Universe . . . . . . . . . . . . . . . . . . . 58
4.3.3 Radiation Dominated Universe. . . . . . . . . . . . . . . . . 60
4.3.4 Vacuum Dominated Universe. . . . . . . . . . . . . . . . . . 61
4.4 Basic Properties of the FRW Metric . . . . . . . . . . . . . . . . . . . 62
4.5 Age of the Universe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.6 ΛCDM Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.7 Destiny of the Universe. . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5 Kinetics and Thermodynamics in Cosmology. . . . . . . . . . . . . . . . 71
5.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2 Thermal Equilibrium in the Early Universe . . . . . . . . . . . . . . 71
5.2.1 General Features. . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.2.2 Kinetic Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . 76
5.2.3 Plasma Heating and Entropy Conservation. . . . . . . . . 80
5.3 Freezing of Species. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
5.3.1 Decoupling and Gershtein-Zeldovich Bound. . . . . . . . 82
5.3.2 Freezing of Non-relativistic Particles. . . . . . . . . . . . . 86
5.4 Neutrino Spectrum and Effective Number
of Neutrino Species. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Contents ix
6 Inflation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.1 Introduction and History . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
6.2 Problems of Pre-inflationary Cosmology . . . . . . . . . . . . . . . . 94
6.2.1 Kinematics and Main Features of Inflation. . . . . . . . . 95
6.2.2 Flatness Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2.3 Horizon Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 96
6.2.4 Origin of the Cosmological Expansion. . . . . . . . . . . . 98
6.2.5 Smoothing Down the Universe and Creation
of Primordial Density Perturbations. . . . . . . . . . . . . . 98
6.2.6 Magnetic Monopole Problem . . . . . . . . . . . . . . . . . . 99
6.3 Mechanisms of Inflation . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.3.1 Canonical Scalar Inflaton with Power
Law Potential. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101
6.3.2 Other Mechanisms of Inflation. . . . . . . . . . . . . . . . . 103
6.4 Universe Heating . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
6.4.1 Perturbative Production . . . . . . . . . . . . . . . . . . . . . . 106
6.4.2 Non-perturbative Phenomena . . . . . . . . . . . . . . . . . . 109
6.4.3 Parametric Resonance . . . . . . . . . . . . . . . . . . . . . . . 112
6.4.4 Particle Production in a Gravitational Field . . . . . . . . 115
6.5 Generation of Gravitational Waves . . . . . . . . . . . . . . . . . . . . 117
6.6 Generation of Density Perturbations . . . . . . . . . . . . . . . . . . . 121
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
7 Baryogenesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.1 Observational Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127
7.2 General Features of Baryogenesis Models . . . . . . . . . . . . . . . 129
7.2.1 Sakharov Principles. . . . . . . . . . . . . . . . . . . . . . . . . 129
7.2.2 CP Breaking in Cosmology . . . . . . . . . . . . . . . . . . . 131
7.3 Models of Baryogenesis. . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
7.3.1 Baryogenesis by Heavy Particle Decays. . . . . . . . . . . 133
7.3.2 Electroweak Baryogenesis . . . . . . . . . . . . . . . . . . . . 135
7.3.3 Baryo-Through-Leptogenesis . . . . . . . . . . . . . . . . . . 138
7.3.4 Evaporation of Primordial Black Holes . . . . . . . . . . . 139
7.3.5 Spontaneous Baryogenesis. . . . . . . . . . . . . . . . . . . . 143
7.3.6 Baryogenesis by Condensed Scalar Baryons. . . . . . . . 149
7.4 Cosmological Antimatter . . . . . . . . . . . . . . . . . . . . . . . . . . . 151
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 156
8 Big Bang Nuclesynthesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161
8.1 Light Elements in the Universe. . . . . . . . . . . . . . . . . . . . . . . 162
8.2 Freeze-Out of Weak Interactions. . . . . . . . . . . . . . . . . . . . . . 163
8.3 Electron-Positron Annihilation . . . . . . . . . . . . . . . . . . . . . . . 165
8.4 Deuterium Bottleneck . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 166
x Contents
8.5 Primordial Nucleosynthesis . . . . . . . . . . . . . . . . . . . . . . . . . 168
8.6 Baryon Abundance. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
8.7 Constraints on New Physics. . . . . . . . . . . . . . . . . . . . . . . . . 171
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173
9 Dark Matter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 175
9.1 Observational Evidence. . . . . . . . . . . . . . . . . . . . . . . . . . . . 176
9.2 Dark Matter Candidates. . . . . . . . . . . . . . . . . . . . . . . . . . . . 178
9.2.1 Lightest Supersymmetric Particle . . . . . . . . . . . . . . . 180
9.2.2 Axion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 181
9.2.3 Super-Heavy Particles . . . . . . . . . . . . . . . . . . . . . . . 181
9.2.4 Primordial Black Holes . . . . . . . . . . . . . . . . . . . . . . 182
9.3 Direct Search for Dark Matter Particles . . . . . . . . . . . . . . . . . 183
9.4 Indirect Search for Dark Matter Particles. . . . . . . . . . . . . . . . 187
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 188
10 Cosmic Microwave Background . . . . . . . . . . . . . . . . . . . . . . . . . 191
10.1 Recombination and Decoupling . . . . . . . . . . . . . . . . . . . . . . 192
10.2 Formalism for the Description of Fluctuations . . . . . . . . . . . . 193
10.3 Anisotropies of the CMB. . . . . . . . . . . . . . . . . . . . . . . . . . . 198
10.3.1 Primary Anisotropies. . . . . . . . . . . . . . . . . . . . . . . . 198
10.3.2 Secondary Anisotropies. . . . . . . . . . . . . . . . . . . . . . 200
10.3.3 Polarization Anisotropies. . . . . . . . . . . . . . . . . . . . . 200
10.4 Primordial Perturbations. . . . . . . . . . . . . . . . . . . . . . . . . . . . 203
10.5 Determination of the Cosmological Parameters. . . . . . . . . . . . 204
Problems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205
11 Dark Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207
11.1 Cosmological Acceleration. . . . . . . . . . . . . . . . . . . . . . . . . . 207
11.1.1 Astronomical Data . . . . . . . . . . . . . . . . . . . . . . . . . 209
11.1.2 Acceleration by a Scalar Field . . . . . . . . . . . . . . . . . 211
11.1.3 Modified Gravity . . . . . . . . . . . . . . . . . . . . . . . . . . 212
11.2 Problem of Vacuum Energy. . . . . . . . . . . . . . . . . . . . . . . . . 213
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
12 Density Perturbations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 217
12.1 Density Perturbations in Newtonian Gravity. . . . . . . . . . . . . . 217
12.2 Density Perturbations in General Relativity . . . . . . . . . . . . . . 223
12.2.1 Metric and Curvature . . . . . . . . . . . . . . . . . . . . . . . 223
12.2.2 Energy-Momentum Tensor. . . . . . . . . . . . . . . . . . . . 224
12.2.3 Choice of Gauge. . . . . . . . . . . . . . . . . . . . . . . . . . . 225