Introduction To The Theory Of The Early Universe: Hot Big Bang Theory (Second Edition)

by Valery A Rubakov, Dmitry S Gorbunov

Overview

This book is written from the viewpoint that a deep connection exists between cosmology and particle physics. It presents the results and ideas on both the homogeneous and isotropic Universe at the hot stage of its evolution and in later stages. The main chapters describe in a systematic and pedagogical way established facts and concepts on the early and the present Universe. The comprehensive treatment, hence, serves as a modern introduction to this rapidly developing field of science. To help in reading the chapters without having to constantly consult other texts, essential materials from General Relativity and the theory of elementary particles are collected in the appendices. Various hypotheses dealing with unsolved problems of cosmology, and often alternative to each other, are discussed at a more advanced level. These concern dark matter, dark energy, matter-antimatter asymmetry, etc.Particle physics and cosmology underwent rapid development between the first and the second editions of this book. In the second edition, many chapters and sections have been revised, and numerical values of particle physics and cosmological parameters have been updated.

Product Details

ISBN-13:	9789813209879
Publisher:	World Scientific Publishing Company, Incorporated
Publication date:	08/23/2017
Pages:	596
Product dimensions:	6.80(w) x 9.70(h) x 0.90(d)

Table of Contents

Preface to the 2nd Edition vii

Preface to the 1st Edition ix

1 Cosmology: A Preview 1

1.1 Units 1

1.2 The Universe Today 3

1.2.1 Homogeneity and isotropy 4

1.2.2 Expansion 4

1.2.3 Age of the Universe and size of its observable part 9

1.2.4 Spatial flatness 10

1.2.5 "Warm" Universe 10

1.3 Energy Balance in the Present Universe 14

1.4 Future of the Universe 19

1.5 Universe in the Past 21

1.5.1 Recombination 21

1.5.2 Big Bang Nucleosynthesis (BBN) 22

1.5.3 Neutrino decoupling 23

1.5.4 Cosmological phase transitions 24

1.5.5 Generation of baryon asymmetry 25

1.5.6 Generation of dark matter 26

1.6 Structure Formation in the Universe 26

1.7 Before the Hot Epoch 28

1.7.1 Argument from observations 28

1.7.2 Drawbacks of the Hot Big Bang theory 30

1.8 Inflationary Theory 31

1.8.1 Alternatives to inflation 32

2 Homogeneous Isotropic Universe 35

2.1 Homogeneous Isotropic Spaces 35

2.2 Friedmann-Lemaître-Robertson-Walker Metric 38

2.3 Redshift. Hubble Law 40

2.4 Slowing Down of Relative Motion 44

2.5 Gases of Free Particles in Expanding Universe 47

3 Dynamics of Cosmological Expansion 51

3.1 Friedmann Equation 51

3.2 Sample Cosmological Solutions. Age of the Universe. Cosmological Horizon 55

3.2.1 Non-relativistic matter ("dust") 56

3.2.2 Relativistic matter ("radiation") 58

3.2.3 Vacuum 60

3.2.4 General barotropic equation of state p = wp 63

3.3 Solutions with Recollapse 64

4 ACDM: Cosmological Model with Dark Matter and Dark Energy 67

4.1 Composition of the Present Universe 67

4.2 General Properties of Cosmological Evolution 70

4.3 Transition from Deceleration to Acceleration 71

4.4 Transition from Radiation Domination to Matter Domination 72

4.5 Present Age of the Universe and Horizon Size 76

4.6 Brightness-Redshift Relation for Distant Standard Candles 79

4.7 Angular Sizes of Distant Objects 88

4.8 *Quintessence 92

4.8.1 Evolution of scalar field in expanding Universe 92

4.8.2 Accelerated cosmological expansion due to scalar field 96

4.8.3 Tracker field 98

5 Thermodynamics in Expanding Universe 101

5.1 Distribution Functions for Bosons and Fermions 101

5.2 Entropy in Expanding Universe. Baryon-to-Photon Ratio 109

5.3 *Models with Intermediate Matter Dominated Stage: Entropy-Generation 113

5.4 *Inequilibrium Processes 118

6 Recombination 123

6.1 Recombination Temperature in Equilibrium Approximation 123

6.2 Photon Last Scattering in Real Universe 128

6.3 *Kinetic Equilibrium 138

6.3.1 Energy transfer from photons to electrons 139

6.3.2 Coulomb scattering: thermal equilibrium of electron-proton component 142

6.3.3 Thermal (in)equilibrium of photons 144

6.4 Horizon at Recombination and its Present Angular Size. Spatial Flatness of the Universe 152

7 Relic Neutrinos 159

7.1 Neutrino Freeze-Out Temperature 159

7.2 Effective Neutrino Temperature. Cosmological Bound on Neutrino Mass 161

7.3 Sterile Neutrinos as Dark Matter Candidates 165

8 Big Bang Nucleosynthesis 179

8.1 Neutron Freeze-Out. Neutron-Proton Ratio 179

8.2 Beginning of Nucleosynthesis. Direction of Nuclear Reactions. Primordial ⁴He 184

8.3 Kinetics of Nucleosynthesis 190

8.3.1 Neutron burning, p + n → D + γ 191

8.3.2 Deuterium burning 192

8.3.3 Primordial ³He and ³H 199

8.3.4 *Production and burning of the heaviest elements in primordial plasma 202

8.4 Comparison of Theory with Observations 205

9 Dark Matter 209

9.1 Cold, Hot and Warm Dark Matter 210

9.2 Freeze-Out of Heavy Relic 213

9.3 Weakly Interacting Massive Particles, WIMPs 223

9.4 *Other Applications of the Results of Section 9.2 230

9.4.1 Residual baryon density in baryon-symmetric Universe 230

9.4.2 Heavy neutrino 231

9.5 Dark Matter Candidates in Particle Physics 232

9.6 *Stable Particles in Super symmetric Models 233

9.6.1 Neutralino 235

9.6.2 Sneutrino 244

9.6.3 Gravitino 244

9.7 Axions and Other Long-lived Particles 255

9.8 Other Candidates 270

9.8.1 *Superheavy relic particles 271

9.8.2 Exotica 272

10 Phase Transitions in the Early Universe 273

10.1 Order of Phase Transition 275

10.2 Effective Potential in One-Loop Approximation 287

10.3 Infrared Problem 300

10.4 *Electroweak Vaccum at Zero Temperature 305

11 Generation of Baryon Asymmetry 313

11.1 Necessary Conditions for Baryogenesis 314

11.2 Baryon and Lepton Number Violation in Particle Interactions 317

11.2.1 Electroweak mechanism 318

11.2.2 Baryon number violation in Grand Unified Theories 324

11.2.3 Violation of lepton numbers and Majorana masses of neutrino 333

11.3 Asymmetry Generation in Particle Decays 335

11.4 Baryon Asymmetry and Neutrino Masses: Leptogenesis 345

11.5 Electroweak Baryogenesis 352

11.5.1 Departure from thermal equilibrium 352

11.5.2 *Thick wall baryogenesis 354

11.5.3 *Thin wall case 360

11.5.4 Electroweak baryogenesis, CP-violation and neutron EEM 366

11.6 *Affleck-Dine Mechanism 367

11.6.1 Scalar fields carrying baryon number 367

11.6.2 Asymmetry generation 369

11.7 Concluding Remarks 375

12 Topological Defects and Solitons in the Universe 377

12.1 Production of Topological Defects in the Early Universe 378

12.2 't Hooft-Polyakov Monopoles 379

12.2.1 Magnetic monopoles in gauge theories 379

12.2.2 Kibble mechanism 383

12.2.3 Residual abundance: the monopole problem 384

12.3 Cosmic Strings 386

12.3.1 String solutions 386

12.3.2 Gas of cosmic strings 394

12.3.3 Deficit angle 396

12.3.4 Strings in the Universe 401

12.4 Domain Walls 405

12.5 *Textures 408

12.6 *Hybrid Topological Defects 411

12.7 *Non-topological Solitons: Q-balls 412

12.7.1 Two-field model 412

12.7.2 Models with fiat directions 418

13 Color Pages 429

Appendix A Elements of General Relativity 443

A.1 Tensors in Curved Space-Time 443

A.2 Covariant Derivative 447

A.3 Riemann Tensor 452

A.4 Gravitational Field Equations 456

A.5 Conformally Related Metrics 461

A.6 Interaction of Matter with Gravitational Field. Energy-Momentum Tensor 464

A.7 Particle Motion in Gravitational Field 470

A.8 Newtonian Limit in General Relativity 473

A.9 Linearized Einstein Equations about Minkowski Background 476

A.10 Macroscopic Energy-Momentum Tensor 477

A.11 Notations and Conventions 478

Appendix B Standard Model of Particle Physics 481

B.1 Field Content and Lagrangian 481

B.2 Global Symmetries 492

B.3 C-, P-, T-Transformations 494

B.4 Quark Mixing 495

B.5 Effective Fermi Theory 501

B.6 Peculiarities of Strong Interactions 502

B.7 The Effective Number of Degrees of Freedom in the Standard Model 503

Appendix C Neutrino Oscillations 505

C.1 Oscillations and Mixing 505

C.1.1 Vacuum oscillations 505

C.1.2 Three-neutrino oscillations in special cases 509

C.1.3 Mikheev-Smirnov-Wolfenstein effect 512

C.2 Experimental Discoveries 514

C.2.1 Solar neutrinos and KamLAND 514

C.2.2 Atmospheric neutrinos, K2K and MINOS 522

C.2.3 Accelerator and reactor neutrinos: |U_es 524

C.3 Osculation Parameters 525

C.4 Dirac and Majorana Masses. Sterile Neutrinos 528

C.5 Search for Neutrino Masses 535

Appendix D Quantum Field Theory at Finite Temperature 537

D.1 Bosonic Fields: Euclidean Time and Periodic Boundary Conditions 537

D.2 Fermionic Fields: Antiperiodic Boundary Conditions 541

D.3 Perturbation Theory 545

D.4 One-Loop Effective Potential 548

D.5 Debye Screening 553

Bibliography 557

Books and Reviews 569

Index 575