现代宇宙学
1 The Standard Model and Beyond
1.1 The Expanding Universe
1.2 The Hubble Diagram
1.3 Big Bang Nucleosynthesis
1.4 The Cosmic Microwave Background
1.5 Beyond the Standard Model
1.6 Summary
Exercises
2 The Smooth, Expanding Universe
2.1 General Relativity
2.1.1 The Metric
2.1.2 The Geodesic Equation
2.1.3 Einstein Equations
2.2 Distances
2.3 Evolution of Energy
2.4 Cosmic Inventory
2.4.1 Photons
2.4.2 Baryons
2.4.3 Matter
2.4.4 Neutrinos
2.4.5 Dark Energy
2.4.6 Epoch of Matter-Radiation Equality
2.5 Summary
Exercises
3 Beyond Equilibrium
3.1 Boltzmann Equation for Annihilation
3.2 Big Bang Nucleosynthesis
3.2.1 Neutron Abundance
3.2.2 Light Element Abundances
3.3 Recombination
3.4 Dark Matter
3.5 Summary
Exercises
4 The Boltzmann Equations
4.1 The Boltzmann Equation for the Harmonic Oscillator
4.2 The Collisionless Boltzmann Equation for Photons
4.2.1 Zero-Order Equation
4.2.2 First-Order Equation
4.3 Collision Terms: Compton Scattering
4.4 The Boltzmann EqUation for Photons
4.5 The Boltzmann Equation for Cold Dark Matter
4.6 The Boltzmann Equation for Baryons
4.7 Summary
Exercises
5 Einstein Equations
5.1 The Perturbed Ricci Tensor and Scalar
5.1.1 Christoffel Symbols
5.1.2 Ricci Tensor
5.2 Two Components of the Einstein Equations
5.3 Tensor Perturbations
5.3.1 Christoffel Symbols for Tensor Perturbations
5.3.2 Ricci Tensor for Tensor Perturbations
5.3.3 Einstein Equations for Tensor Perturbations
5.4 The Decomposition Theorem
5.5 From Gauge to Gauge
5.6 Summary
Exercises
6 Initial Conditions
6.1 The Einstein-Boltzmann Equations at Early Times
6.2 The Horizon
6.3 Inflation
6.3.1 A Solution to the Horizon Problem
6.3.2 Negative Pressure
6.3.3 Implementation with a Scalar Field
6.4 Gravity Wave Production
6.4.1 Quantizing the Harmonic Oscillator
6.4.2 Tensor Perturbations
6.5 Scalar Perturbations
6.5.1 Scalar Field Perturbations around a Smooth Background
6.5.2 Super-Horizon Perturbations
6.5.3 Spatially Flat Slicing
6.6 Summary and Spectral Indices
Exercises
7 Inhomogeneities
7.1 Prelude
7.1.1 Three Stages of Evolution
7.1.2 Method
7.2 Large Scales
7.2.1 Super-horizon Solution
7.2.2 Through Horizon Crossing
7.3 Small Scales
7.3.1 Horizon Crossing
7.3.2 Sub-horizon Evolution
7.4 Numerical Results and Fits
7.5 Growth Function
7.6 Beyond Cold Dark Matter
7.6.1 Baryons
7.6.2 Massive Neutrinos
7.6.3 Dark Energy
Exercises
8 Anisotropies
8.1 Overview
8.2 Large-Scale Anisotropies
8.3 Acoustic Oscillations
8.3.1 Tightly Coupled Limit of the Boltzmann Equations
8.3.2 Tightly Coupled Solutions
8.4 Diffusion Damping
8.5 Inhomogeneities to Anisotropies
8.5.1 Free Streaming
8.5.2 The Cls
8.6 The Anisotropy Spectrum Today
8.6.1 Sachs-Wolfe Effect
8.6.2 Small Scales
8.7 Cosmological Parameters
8.7.1 Curvature
8.7.2 Degenerate Parameters
8.7.3 Distinct Imprints
Exercises
9 Probes of Inhomogeneities
9.1 Angular Correlations
9.2 Peculiar Velocities
9.3 Direct Measurements of Peculiar Velocities
9.4 Redshift Space Distortions
9.5 Galaxy Clusters
Exercises
10 Weak Lensing and Polarization
10.1 Gravitational Distortion of Images
10.2 GeodesiCs and Shear
10.3 Ellipticity as an Estimator of Shear
10.4 Weak Lensing Power Spectrum
10.5 Polarization: The Quadrupole and the Q/U DecompositioI
10.6 Polarization from a Single Plane Wave
10.7 Boltzmann Solution
10.8 Polarization Power Spectra
10.9 Detecting Gravity Waves
Exercises
11 Analysis
11.1 The Likelihood Function
11.1.1 Simple Example
11.1.2 CMB Likelihood
11.1.3 Galaxy Surveys
11.2 Signal Covariance Matrix
11.2.1 CMB Window Functions
11.2.2 Examples of CMB Window Functions
11.2.3 Window Functions for Galaxy Surveys
11.2.4 Summary
11.3 Estimating the Likelihood Function
11.3.1 Karhunen-Loeve Techniques
11.3.2 Optimal Quadratic Estimator
11.4 The Fisher Matrix: Limits and Applications
11.4.1 CMB
11.4.2 Galaxy Surveys
11.4.3 Forecasting
11.5 Mapmaking and Inversion
11.6 Systematics
11.6.1 Foregrounds
11.6.2 Mode Subtraction
Exercises
A Solutions to Selected Problems
B Numbers
B.1 Physical Constants
B.2 Cosmological Constants
C Special Functions
C.1 Legendre Polynomials
C.2 Spherical Harmonics
C.3 Spherical Bessel Functions
C.4 Fourier Transforms
C.5 Miscellaneous
D Symbols
Bibliography
Index
1.1 The Expanding Universe
1.2 The Hubble Diagram
1.3 Big Bang Nucleosynthesis
1.4 The Cosmic Microwave Background
1.5 Beyond the Standard Model
1.6 Summary
Exercises
2 The Smooth, Expanding Universe
2.1 General Relativity
2.1.1 The Metric
2.1.2 The Geodesic Equation
2.1.3 Einstein Equations
2.2 Distances
2.3 Evolution of Energy
2.4 Cosmic Inventory
2.4.1 Photons
2.4.2 Baryons
2.4.3 Matter
2.4.4 Neutrinos
2.4.5 Dark Energy
2.4.6 Epoch of Matter-Radiation Equality
2.5 Summary
Exercises
3 Beyond Equilibrium
3.1 Boltzmann Equation for Annihilation
3.2 Big Bang Nucleosynthesis
3.2.1 Neutron Abundance
3.2.2 Light Element Abundances
3.3 Recombination
3.4 Dark Matter
3.5 Summary
Exercises
4 The Boltzmann Equations
4.1 The Boltzmann Equation for the Harmonic Oscillator
4.2 The Collisionless Boltzmann Equation for Photons
4.2.1 Zero-Order Equation
4.2.2 First-Order Equation
4.3 Collision Terms: Compton Scattering
4.4 The Boltzmann EqUation for Photons
4.5 The Boltzmann Equation for Cold Dark Matter
4.6 The Boltzmann Equation for Baryons
4.7 Summary
Exercises
5 Einstein Equations
5.1 The Perturbed Ricci Tensor and Scalar
5.1.1 Christoffel Symbols
5.1.2 Ricci Tensor
5.2 Two Components of the Einstein Equations
5.3 Tensor Perturbations
5.3.1 Christoffel Symbols for Tensor Perturbations
5.3.2 Ricci Tensor for Tensor Perturbations
5.3.3 Einstein Equations for Tensor Perturbations
5.4 The Decomposition Theorem
5.5 From Gauge to Gauge
5.6 Summary
Exercises
6 Initial Conditions
6.1 The Einstein-Boltzmann Equations at Early Times
6.2 The Horizon
6.3 Inflation
6.3.1 A Solution to the Horizon Problem
6.3.2 Negative Pressure
6.3.3 Implementation with a Scalar Field
6.4 Gravity Wave Production
6.4.1 Quantizing the Harmonic Oscillator
6.4.2 Tensor Perturbations
6.5 Scalar Perturbations
6.5.1 Scalar Field Perturbations around a Smooth Background
6.5.2 Super-Horizon Perturbations
6.5.3 Spatially Flat Slicing
6.6 Summary and Spectral Indices
Exercises
7 Inhomogeneities
7.1 Prelude
7.1.1 Three Stages of Evolution
7.1.2 Method
7.2 Large Scales
7.2.1 Super-horizon Solution
7.2.2 Through Horizon Crossing
7.3 Small Scales
7.3.1 Horizon Crossing
7.3.2 Sub-horizon Evolution
7.4 Numerical Results and Fits
7.5 Growth Function
7.6 Beyond Cold Dark Matter
7.6.1 Baryons
7.6.2 Massive Neutrinos
7.6.3 Dark Energy
Exercises
8 Anisotropies
8.1 Overview
8.2 Large-Scale Anisotropies
8.3 Acoustic Oscillations
8.3.1 Tightly Coupled Limit of the Boltzmann Equations
8.3.2 Tightly Coupled Solutions
8.4 Diffusion Damping
8.5 Inhomogeneities to Anisotropies
8.5.1 Free Streaming
8.5.2 The Cls
8.6 The Anisotropy Spectrum Today
8.6.1 Sachs-Wolfe Effect
8.6.2 Small Scales
8.7 Cosmological Parameters
8.7.1 Curvature
8.7.2 Degenerate Parameters
8.7.3 Distinct Imprints
Exercises
9 Probes of Inhomogeneities
9.1 Angular Correlations
9.2 Peculiar Velocities
9.3 Direct Measurements of Peculiar Velocities
9.4 Redshift Space Distortions
9.5 Galaxy Clusters
Exercises
10 Weak Lensing and Polarization
10.1 Gravitational Distortion of Images
10.2 GeodesiCs and Shear
10.3 Ellipticity as an Estimator of Shear
10.4 Weak Lensing Power Spectrum
10.5 Polarization: The Quadrupole and the Q/U DecompositioI
10.6 Polarization from a Single Plane Wave
10.7 Boltzmann Solution
10.8 Polarization Power Spectra
10.9 Detecting Gravity Waves
Exercises
11 Analysis
11.1 The Likelihood Function
11.1.1 Simple Example
11.1.2 CMB Likelihood
11.1.3 Galaxy Surveys
11.2 Signal Covariance Matrix
11.2.1 CMB Window Functions
11.2.2 Examples of CMB Window Functions
11.2.3 Window Functions for Galaxy Surveys
11.2.4 Summary
11.3 Estimating the Likelihood Function
11.3.1 Karhunen-Loeve Techniques
11.3.2 Optimal Quadratic Estimator
11.4 The Fisher Matrix: Limits and Applications
11.4.1 CMB
11.4.2 Galaxy Surveys
11.4.3 Forecasting
11.5 Mapmaking and Inversion
11.6 Systematics
11.6.1 Foregrounds
11.6.2 Mode Subtraction
Exercises
A Solutions to Selected Problems
B Numbers
B.1 Physical Constants
B.2 Cosmological Constants
C Special Functions
C.1 Legendre Polynomials
C.2 Spherical Harmonics
C.3 Spherical Bessel Functions
C.4 Fourier Transforms
C.5 Miscellaneous
D Symbols
Bibliography
Index
Scott Dodelson：美国费米国家实验室理论天体物理研究组负责人和芝加哥大学天文和天体物理学系教授。在哥伦比亚大学获博士学位。进入费米国家实验室和芝加哥大学前在哈佛大学做研究员。在宇宙论方面发表了七十多篇论文，其中大部分是关于宇宙的微波背景和大尺度结构。
目次：标准模型及其它；平坦扩张的宇宙；远离平衡态；波尔兹曼方程；爱因斯坦方程；初始条件；多样性；各项异性；多样性的探测；弱透镜化和偏振；分析；附录A：部分习题解答；附录B：常数；附录C：特殊函数；附录D：符号；参考文献；索引。
读者对象：理论物理、天文物理和宇宙学等专业的高年级本科生、研究生和相关专业的科研人员。
目次：标准模型及其它；平坦扩张的宇宙；远离平衡态；波尔兹曼方程；爱因斯坦方程；初始条件；多样性；各项异性；多样性的探测；弱透镜化和偏振；分析；附录A：部分习题解答；附录B：常数；附录C：特殊函数；附录D：符号；参考文献；索引。
读者对象：理论物理、天文物理和宇宙学等专业的高年级本科生、研究生和相关专业的科研人员。
There are two aspects of cosmology today that make it more alluring than ever. First, there is an enormous amount of data. To give just one example of how rapidly our knowledge of the structure of the universe is advancing, consider galaxy surveys which map the sky. In 1985, the state-of-the-art survey was the one carried out by the Center for Astrophysics; it consisted of the positions of 1100 galaxies. Today, the Sloan Digital Sky Survey and the Two Degree Field between them have recorded the 3D positions of half a million galaxies.
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