宇宙学的物理基础

Foreword by Professor Andrei Linde Preface

Acknowledgements

Units and conventions

Part I Homogeneous isotropic universe

1 Kinematics and dynamics of an expanding universe

1．1 Hubble law

1．2 Dynamics of dust in Newtonian cosmology

1．2．1 Continuity equation

1．2．2 Acceleration equation

1．2．3 Newtonian solutions

1．3 From Newtonian to relativistic cosmology

lForeword by Professor Andrei Linde Preface

Acknowledgements

Units and conventions

Part I Homogeneous isotropic universe

1 Kinematics and dynamics of an expanding universe

1．1 Hubble law

1．2 Dynamics of dust in Newtonian cosmology

1．2．1 Continuity equation

1．2．2 Acceleration equation

1．2．3 Newtonian solutions

1．3 From Newtonian to relativistic cosmology

1．3．1 Geometry of an homogeneous，isotropic space

1．3．2 The Einstein equations and cosmic evolution

1．3．3 Friedmann equations

1．3．4 Conformal time and relativistic solutions

1．3．5 Milne universe

1．3．6 De Sitter universe

2 Propagation of light and horizons

2．1 Light geodesics

2．2 Horizons

2．3 Conformal diagrams

2．4 Redshifl

2．4．1 Redshifl as a measure of time and distance

2．5 Kinematic tests

2．5．1 Angular diameter-redshift relation

2．5．2 Luminosity—redshifl relation

2．5．3 Number counts

2．5．4 Redshift evolution

3 The hot universe

3．1 The composition of the universe

3．2 Brief thermal history

3．3 Rudiments of thermodynamics

3．3．1 Maximal entropy state，thermal spectrum， conservation laws and chemical potentials

3．3．2 Energy density，pressure and the equation of state

3．3．3 Calculating integrals

3．3．4 Ultra—relativistic particles

3．3．5 Nonrelativistic particles

3．4 Lepton era

3．4．1 ChemicaI potentials

3．4．2 Neutrino decoupling and electrOn—pOsitrOn annihilation

3．5 NucleOsvnthesis

3．5．1 Freeze—OUt of neutrons

3．5．2“Deuterium bottleneck”

3．5．3 Helium一4

3．5．4 Deuterium

3．5．5 The other light elements

3．6 Recombination

3．6．1 Helium recombination

3．6．2 Hydrogen recombination：equilibrium consideration

3．6．3 Hydrogen recombination：the kinetic approach

4 The very early universe

4．1 Basics

4．1．1 Local gauge invariance

4．1．2 Non—Abelian gauge theories

4．2 Quantum chromodynamics and quark-gluon plasma

4．2．1 Running coupling constant and asymptotic freedom

4．2．2 Cosmological quark-gluon phase transition

4．3 Electroweak theory

4．3．1 Fermion content

4．3．2“Spontaneous breaking”of U(1)symmetry

4．3．3 Gauge bosons

4．3．4 Fermion interactions

4．3．5 Fermion masses

4．3．6 CP violation

4．4 “Symmetry restoration”and phase transitions

4．4．1 Effective potential

4．4．2 U(l)model

4．4．3 Symmetry restoration at high temperature

4．4．4 Phase transitions

4．4．5 Electroweak phase transition

4．5 Instantons．sphalerons and the early universe

4．5．1 Particle escape from a potential well

4．5．2 Decay of the metastable vacuum

4．5．3 The vacuum structure of gauge theories

4．5．4 Chiral anomaly and nonconservation of the fermion number

4．6 Beyond the Standard Model

4．6．1 Dark matter candidates

4．6．2 Baryogenesis

4．6．3 Topological defects

5 Inflation I：homogeneous limit

5．1 Problem of initial conditions

5．2 Inflation：main idea

5．3 How can gravity become“repulsive”?

5．4 How to realize the equation of state P≈一#####

5．4．1 Simple example：V=m2#4#####

5．4．2 General potential：slow—roll approximation

5．5 Preheating and reheating

5．5．1 Elementary theory

5．5．2 Narrow resonance

5．5．3 Broad resonance

5．5．4 Implications

5．6 “Menu”of scenarios

Part II Inhomogeneous universe

6 Gravitational instability in Newtonian theory

6．1 Basic equations

6．2 Jeans theory

6．2．1 Adiabatic perturbations

6．2．2 Vector perturbations

6．2．3 Entropy perturbations

6．3 Instability in an expanding universe

6．3．1 Adiabatic perturbations

6．3．2 Vector perturbations

6．3．3 Self-similar solution

6．3．4 Cold matter in the presence of radiation or dark energy

6．4 Beyond linear approximation

6．4．1 Tolman solution

6．4．2 Zel’dovich solution

6．4．3 Cosmic web

7 Gravitational instability in General Relativity

7．1 Perturbations and gauge—invariant variables

7．1．1 Classification of perturbations

7．1．2 Gauge transformations and gauge—invariant variables

7．1．3 COOrdinate systems

7．2 Equations for cosmological perturbations

7．3 Hydrodynamical perturbations

7．3．1 Scalar perturbations

7．3．2 Vector and tensor perturbations

7．4 Baryon-radiation plasma and cold dark matter

7．4．1 Equations

7．4．2 Evolution of perturbations and transfer functions

8 Inflation II：origin of the primordial inhomogeneities

8．1 Characterizing perturbations

8．2 Perturbations on inflation(slow—roll approximation)

8．2．1 Inside the Hubble scale

8．2．2 The spectrum of generated perturbations

8．2．3 Why dO we need inflation?

8．3 Quantum cosmological perturbations

8．3．1 Equations

8．3．2 Classical solutions

8．3．3 Quantizing perturbations

8．4 Gravitationa waves from inflation

8．5 Self_reDroductiOn of the universe

8．6 Infation as a theory with predictive power

9 Cosmic microwave background anisotropies

9．1 Basics

9．2 Sachs-Wolfe eflfect

9．3 Initial conditions

9．4 Correlation function and multipoles

9．5 Anisotropies on large angular scales

9．6 Delayed recombination and the finite thickness effect

9．7 Anisotropies on small angular scales

9．7．1 Transfer functions

9．7．2 Multipole moments

9．7．3 Parameters

9．7．4 Calculating the spectrum

9．8 Determining cosmic parameters

9．9 Gravitational waves

9．10 Polarization of the cosmic microwave background

9．10．1 Polarization tensor

9．10．2 Thomson scattering and polarization

9．10．3 Delayed recombination and polarization

9．10．4 E and B polarization modes and correlation functions

9．1l Reionization

Bibliography

Expanding universe(Chapters 1 and 2)

Hot universe and nucleosvnthesis(Chapter 3)

Particle physics and early universe(Chapter 4)

Inflation (Chapters 5 and 8)

Gravitational instability(Chapters 6 and 7)

CMB fluctuations(Chapter 9)

lndex

3．1 Geometry of an homogeneous，isotropic space

1．3．2 The Einstein equations and cosmic evolution

1．3．3 Friedmann equations

1．3．4 Conformal time and relativistic solutions

1．3．5 Milne universe

1．3．6 De Sitter universe

2 Propagation of light and horizons

2．1 Light geodesics

2．2 Horizons

2．3 Conformal diagrams

2．4 Redshifl

2．4．1 Redshifl as a measure of time and distance

2．5 Kinematic tests

2．5．1 Angular diameter-redshift relation

2．5．2 Luminosity—redshifl relation

2．5．3 Number counts

2．5．4 Redshift evolution

3 The hot universe

3．1 The composition of the universe

3．2 Brief thermal history

3．3 Rudiments of thermodynamics

3．3．1 Maximal entropy state，thermal spectrum， conservation laws and chemical potentials

3．3．2 Energy density，pressure and the equation of state

3．3．3 Calculating integrals

3．3．4 Ultra—relativistic particles

3．3．5 Nonrelativistic particles

3．4 Lepton era

3．4．1 ChemicaI potentials

3．4．2 Neutrino decoupling and electrOn—pOsitrOn annihilation

3．5 NucleOsvnthesis

3．5．1 Freeze—OUt of neutrons

3．5．2“Deuterium bottleneck”

3．5．3 Helium一4

3．5．4 Deuterium

3．5．5 The other light elements

3．6 Recombination

3．6．1 Helium recombination

3．6．2 Hydrogen recombination：equilibrium consideration

3．6．3 Hydrogen recombination：the kinetic approach

4 The very early universe

4．1 Basics

4．1．1 Local gauge invariance

4．1．2 Non—Abelian gauge theories

4．2 Quantum chromodynamics and quark-gluon plasma

4．2．1 Running coupling constant and asymptotic freedom

4．2．2 Cosmological quark-gluon phase transition

4．3 Electroweak theory

4．3．1 Fermion content

4．3．2“Spontaneous breaking”of U(1)symmetry

4．3．3 Gauge bosons

4．3．4 Fermion interactions

4．3．5 Fermion masses

4．3．6 CP violation

4．4 “Symmetry restoration”and phase transitions

4．4．1 Effective potential

4．4．2 U(l)model

4．4．3 Symmetry restoration at high temperature

4．4．4 Phase transitions

4．4．5 Electroweak phase transition

4．5 Instantons．sphalerons and the early universe

4．5．1 Particle escape from a potential well

4．5．2 Decay of the metastable vacuum

4．5．3 The vacuum structure of gauge theories

4．5．4 Chiral anomaly and nonconservation of the fermion number

4．6 Beyond the Standard Model

4．6．1 Dark matter candidates

4．6．2 Baryogenesis

4．6．3 Topological defects

5 Inflation I：homogeneous limit

5．1 Problem of initial conditions

5．2 Inflation：main idea

5．3 How can gravity become“repulsive”?

5．4 How to realize the equation of state P≈一#####

5．4．1 Simple example：V=m2#4#####

5．4．2 General potential：slow—roll approximation

5．5 Preheating and reheating

5．5．1 Elementary theory

5．5．2 Narrow resonance

5．5．3 Broad resonance

5．5．4 Implications

5．6 “Menu”of scenarios

Part II Inhomogeneous universe

6 Gravitational instability in Newtonian theory

6．1 Basic equations

6．2 Jeans theory

6．2．1 Adiabatic perturbations

6．2．2 Vector perturbations

6．2．3 Entropy perturbations

6．3 Instability in an expanding universe

6．3．1 Adiabatic perturbations

6．3．2 Vector perturbations

6．3．3 Self-similar solution

6．3．4 Cold matter in the presence of radiation or dark energy

6．4 Beyond linear approximation

6．4．1 Tolman solution

6．4．2 Zel’dovich solution

6．4．3 Cosmic web

7 Gravitational instability in General Relativity

7．1 Perturbations and gauge—invariant variables

7．1．1 Classification of perturbations

7．1．2 Gauge transformations and gauge—invariant variables

7．1．3 COOrdinate systems

7．2 Equations for cosmological perturbations

7．3 Hydrodynamical perturbations

7．3．1 Scalar perturbations

7．3．2 Vector and tensor perturbations

7．4 Baryon-radiation plasma and cold dark matter

7．4．1 Equations

7．4．2 Evolution of perturbations and transfer functions

8 Inflation II：origin of the primordial inhomogeneities

8．1 Characterizing perturbations

8．2 Perturbations on inflation(slow—roll approximation)

8．2．1 Inside the Hubble scale

8．2．2 The spectrum of generated perturbations

8．2．3 Why dO we need inflation?

8．3 Quantum cosmological perturbations

8．3．1 Equations

8．3．2 Classical solutions

8．3．3 Quantizing perturbations

8．4 Gravitationa waves from inflation

8．5 Self_reDroductiOn of the universe

8．6 Infation as a theory with predictive power

9 Cosmic microwave background anisotropies

9．1 Basics

9．2 Sachs-Wolfe eflfect

9．3 Initial conditions

9．4 Correlation function and multipoles

9．5 Anisotropies on large angular scales

9．6 Delayed recombination and the finite thickness effect

9．7 Anisotropies on small angular scales

9．7．1 Transfer functions

9．7．2 Multipole moments

9．7．3 Parameters

9．7．4 Calculating the spectrum

9．8 Determining cosmic parameters

9．9 Gravitational waves

9．10 Polarization of the cosmic microwave background

9．10．1 Polarization tensor

9．10．2 Thomson scattering and polarization

9．10．3 Delayed recombination and polarization

9．10．4 E and B polarization modes and correlation functions

9．1l Reionization

Bibliography

Expanding universe(Chapters 1 and 2)

Hot universe and nucleosvnthesis(Chapter 3)

Particle physics and early universe(Chapter 4)

Inflation (Chapters 5 and 8)

Gravitational instability(Chapters 6 and 7)

CMB fluctuations(Chapter 9)

lndex

This book is meant to be neither encyclopedic nor a sourcebook for the most recent observational data. In fact, I avoid altogether the presentation of data; after all the data change very quickly and are easily accessible from numerous available monographs as well as on the Intemet. Furthermore, I have intentionally restricted the discussion in this book to results that have a solid basis. I believe it is premature to present detailed mathematical consideration of controversial topics in a book on the foundations of cosmology and, therefore, such topics are covered only at a very elementary level.