现代宇宙学

章节摘录

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前言

The Men of the Great Assembly had three sayings: "Be patient before reachinga decision; Enable many students to stand on their own; Make a fence around yourteaching."Ethics of the Fathers 1:1There 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 rapidlyour knowledge of the structure of the universe is advancing, consider galaxy surveyswhich map the sky. In 1985, the state-of-the-art survey was the one carried out bythe Center for Astrophysics; it consisted of the positions of 1100 galaxies. Today, theSloan Digital Sky Survey and the Two Degree Field between them have recordedthe 3D positions of half a million galaxies.The other aspect of modern cosmology which distinguishes it from previousefforts to understand the universe is that we have developed a consistent theoret-ical framework which agrees quantitatively with the data. These two features arethe secret of the excitement in modern cosmology: we have a theory which makespredictions, and these predictions can be tested by observations. Understanding what the theory is and what predictions it makes is not trivial.First, many of the predictions are statistical. We don't predict that there should bea hot spot in the cosmic microwave background （CMB） at RA = 15h, dec= 27~~~~.Rather, predictions are about the distribution and magnitude of hot and cold spots.Second, these predictions, and the theory on which they are based, involve lots ofsteps, many arguments drawn from a broad range of physics. For example, wewill see that the distribution of hot and cold spots in the CMB depends on quan-tum mechanics, general relativity, fluid dynamics, and the interaction of light withmatter. So we will indeed follow the first dictum of the Men of the Great Assem-bly and be patient before coming to judgment. Indeed, the fundamental measuresof structure in the universe——the power spectra of matter and radiation——agreeextraordinary well with the current cosmological theory, but we won't have thetools to understand this agreement completely until Chapters 7 and 8. Sober mindshave always knows that it pays to be patient before pronouncing judgment on ideasas lofty as those necessary to understand our Universe. The modern twist on this"Be patient" theme is that we need to set up the framework （in this case Chapters.

内容概要

作者：(英国)都德尔逊 (Scott Dodelson)

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。

书籍目录

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

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

5.3.2 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 Cl's

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 Decomposition

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

编辑推荐

《现代宇宙学》的特色：（1）讲解了现代宇宙学的理论基础，处理方法和具体解释，阐明了当前在宇宙学研究中的深刻思想；（2）涵盖了过去十年中在宇宙学研究中的重大进展；（3）包括了上百幅很有特色的教学图片。

作者简介

《现代宇宙学》系统地介绍了现代宇宙学的最新进展。从平坦均匀的宇宙（可以用弗里德曼—罗伯逊—沃克度规描述）开始，讲解了暗能量的处理过程，宇宙大爆炸的核合成，重组和暗物质，然后介绍了对平坦均匀宇宙的扰动：宇宙的演化和爱因斯坦—玻尔兹曼方程组，原始膨胀和现代宇宙的形成，以及观测结果如宇宙微波背景的各向异性，红移扭曲和弱透镜化现象等。《现代宇宙学》对宇宙微波背景的声学峰结构，以及用来探测原始引力波的偏振的E/B分解都有较详细的讨论，还包含了一个长的章节专门介绍对日益庞大的宇宙观测数据进行现代分析的技术。每章后都附有该章总结和相关文献。通过学习，读者可以获得从事现代宇宙学研究必须的知识和方法。

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