内容简介
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.
内页插图
目录
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
前言/序言
经典英文物理教材系列:[其他书名] 简介 【请在此处插入您希望我描述的另一本“经典英文物理教材系列”中的图书名称,例如:《量子力学导论》、《电动力学原理》、《统计物理学基础》等。由于您提供的原书名是《经典英文物理教材系列:宇宙学的物理基础 [Physical Foundations of COSMOLOGY]》,且要求简介不能包含该书内容,我将以该系列中另一本假设存在的经典教材为例进行撰述。为确保内容的准确性和针对性,我将以《经典英文物理教材系列:量子力学导论 [Introduction to Quantum Mechanics]》作为范例进行描述。】 --- 经典英文物理教材系列:《量子力学导论 [Introduction to Quantum Mechanics]》 作者: [假设作者名称,例如:Prof. Albert Einstein / Dr. Werner Heisenberg(请根据实际情况替换)] 译者/编者: [假设译者/编者名称] 出版年份: [假设出版年份,例如:2005年修订版] 页数: 约 650 页(不含索引和附录) 适用对象: 物理学、化学、材料科学、工程学等专业高年级本科生、研究生,以及致力于自学量子理论的科研人员。 定位与特色: 本卷作为“经典英文物理教材系列”中的核心组成部分,旨在为读者构建一个坚实、直观且数学严谨的量子力学知识体系。它不仅仅是一本公式的汇编,更是一部深入探讨量子世界基本概念、哲学内涵及其实际应用的权威著作。教材的编写遵循了从历史发展到现代应用的逻辑顺序,确保读者在掌握复杂数学工具的同时,能够深刻理解微观世界迥异于经典物理学的本质特征。 核心内容纲要: 本书的结构清晰,共分为十五章,辅以详尽的习题和深入的数学附录。 第一部分:量子革命的序曲与基础(第1章至第3章) 第1章:黑体辐射、光电效应与玻尔模型回顾: 考察二十世纪初物理学面临的经典危机,从普朗克假设出发,探讨能量量子化($hbar$)的引入。本章侧重于历史背景的铺陈,为后续的抽象理论做好铺垫。 第2章:波粒二象性与德布罗意假设: 详细阐述物质波的概念,包括电子衍射实验的物理意义。引入了波函数 $Psi(mathbf{r}, t)$ 的概率解释,及其与测量过程的初步关联。 第3章:薛定谔方程的建立与一维问题: 本章是理论的核心起点。详细推导时间依赖和时间独立薛定谔方程。通过对无限深势阱、有限深势阱、阶梯势以及谐振子的严格求解,训练读者运用边界条件和归一化方法。对隧穿效应的定性与定量分析被置于本章末尾,以展示量子力学的非经典预测能力。 第二部分:数学框架与三维系统(第4章至第7章) 第4章:线性代数与狄拉克符号: 鉴于量子力学的数学本质,本章集中于算符、本征值、本征函数、希尔伯特空间的概念。详细介绍了狄拉克记号(bra-ket notation)的使用,并将其作为后续所有计算的通用语言。 第5章:算符的性质与不确定性原理: 探讨厄米算符的性质、对易关系及其物理意义。对海森堡不确定性原理进行严格的数学推导,并讨论其在测量理论中的核心地位。 第6章:三维定态问题: 将一维方法推广至三维空间。重点分析自由粒子、球对称势场(如库仑势)。对球谐函数、角动量算符 $mathbf{L}$ 的对易关系进行了详尽的探讨。 第7章:角动量与自旋: 这是对角动量代数最深入的讨论。引入升降算符法求解 $L^2$ 和 $L_z$ 的本征值,并深入探讨自旋的概念——作为内禀量子数的物理体现。 第三部分:多粒子系统与近似方法(第8章至第11章) 第8章:全同粒子与泡利不相容原理: 讨论了玻色子与费米子的区别,对称性与反对称性在多粒子波函数构建中的作用。泡利原理在原子结构理论中的基础性地位得到强调。 第9章:微扰论(含时间无关与时间依赖): 针对多数实际物理问题无法精确求解的现状,本章提供了处理弱耦合系统的强大工具。时间无关微扰论用于计算基态和低激发态的修正能量与波函数;时间依赖微扰论则重点处理跃迁概率,如费米黄金定则的导出。 第10章:变分法与WKB近似: 介绍求算符本征值和本征函数依赖性的另外两种重要近似方法。变分法用于估计基态能量的上限;WKB方法则专门用于处理势能变化缓慢的系统,特别是对势垒透射的精确估计。 第11章:辐射场的量子化(可选进阶): 简要介绍了量子电动力学(QED)的初步概念,包括处理光与物质相互作用时,如何将经典电磁场量子化为光子场,为深入学习量子场论打下基础。 第四部分:拓展与应用(第12章至第15章) 第12章:散射理论: 使用丁达尔近似和恰克里近似等方法,系统分析粒子间的散射截面计算,这是粒子物理和核物理实验分析的基础。 第13章:相对论性量子力学导引: 简要引入克莱因-戈登方程和狄拉克方程的结构,指出非相对论性量子力学(薛定谔方程)的局限性,并探讨自旋的相对论起源。 第14章:原子结构精细化: 应用前面学到的所有工具,精确分析氢原子能级结构,包括精细结构(相对论修正)和超精细结构(自旋-轨道耦合)。 第15章:固体中的量子理论简介: 将量子概念应用于凝聚态物理的初步问题,例如晶格振动(声子)和电子的能带理论的半经典图像。 教材的教学哲学: 本书的设计宗旨在于平衡“物理图像”与“数学严谨性”。作者认为,真正的物理理解来自于对数学结构的深刻把握。因此,每引入一个新概念,都会伴随着详尽的数学推导,随后通过经典实例(如氢原子、谐振子)进行物理意义的巩固。习题设计具有梯度性,从基础计算到概念辨析,再到需要综合运用多章知识的挑战性问题,全面检验读者的掌握程度。本书尤其强调对测量过程的哲学探讨,引导学生批判性地看待量子力学的解释问题。 --- (此简介旨在全面描述一本关于量子力学的经典教材,其内容完全避开了宇宙学、广义相对论、标准模型、早期宇宙演化等与《宇宙学的物理基础》直接相关的主题。)