Preface xi

About the Companion Website xv

1 A Brief History of Cosmological Ideas 1

2 Observational Overview 3

2.1 In visible light 4

2.2 In other wavebands 8

2.3 Homogeneity and isotropy 11

2.4 The expansion of the Universe 11

2.5 Particles in the Universe 14

2.5.1 What particles are there? 14

2.5.2 Thermal distributions and the blackbody spectrum 16

3 Newtonian Gravity 21

3.1 The Friedmann equation 22

3.2 On the meaning of the expansion 25

3.3 Things that go faster than light 25

3.4 The fluid equation 26

3.5 The acceleration equation 27

3.6 On mass, energy, and vanishing factors of c 2 28

4 The Geometry of the Universe 31

4.1 Flat geometry 31

4.2 Spherical geometry 32

4.3 Hyperbolic geometry 35

4.4 Infinite and observable universes 36

4.5 Where did the Big Bang happen? 36

4.6 Three values of k 37

5 Simple Cosmological Models 39

5.1 Hubble's law 39

5.2 Expansion and redshift 40

5.3 Solving the equations 41

5.3.1 Matter 42

5.3.2 Radiation 43

5.3.3 Mixtures 44

5.4 Particle number densities 46

5.5 Evolution including curvature 47

6 Observational Parameters 51

6.1 The expansion rate H 0 51

6.2 The density parameter ¿ 0 53

6.3 The deceleration parameter q0 55

7 The Cosmological Constant 57

7.1 Introducing ¿ 57

7.2 Fluid description of ¿ 58

7.3 Cosmological models with ¿ 60

8 The Age of the Universe 63

9 The Density of the Universe and Dark Matter 69

9.1 Weighing the Universe 69

9.1.1 Counting stars 69

9.1.2 Nucleosynthesis foreshadowed 70

9.1.3 Galaxy rotation curves 71

9.1.4 Galaxy cluster composition 72

9.1.5 The formation of structure 74

9.1.6 The geometry of the Universe and the brightness of supernovae 74

9.2 What might the dark matter be? 76

9.2.1 Fundamental particles 76

9.2.2 Compact objects 78

9.3 Dark matter searches 78

10 The Cosmic Microwave Background 81

10.1 Properties of the microwave background 81

10.2 The photon to baryon ratio 83

10.3 The origin of the microwave background 84

10.4 The origin of the microwave background (optional advanced treatment) 87

11 The Early Universe 91

12 Nucleosynthesis: The Origin of the Light Elements 99

12.1 Hydrogen and helium 100

12.2 Comparing with observations 103

12.3 Contrasting decoupling and nucleosynthesis 105

13 The Inflationary Universe 107

13.1 Problems with the Hot Big Bang 107

13.1.1 The flatness problem 107

13.1.2 The horizon problem 109

13.1.3 Relic particle abundances 111

13.2 Inflationary expansion 111

13.3 Solving the Big Bang problems 113

13.3.1 The flatness problem 113

13.3.2 The horizon problem 114

13.3.3 Relic particle abundances 114

13.4 How much inflation? 115

13.5 Inflation and particle physics 116

14 The Initial Singularity 121

15 Overview: The Standard Cosmological Model 125

15.1 Expansion 126

15.2 Geometry 126

15.3 Age 126

15.4 Fate 126

15.5 127

15.6 Early history 128

15.7 Outlook 128

Advanced Topic 1 General Relativistic Cosmology 129

A. 1 The metric of space-time 129

A1.2 The Einstein equations 131

A1.3 Aside: Topology of the Universe 132

Advanced Topic 2 Classic Cosmology: Distances and Luminosities 135

A2.1 Light propagation and redshift 135

A2.2 The observable Universe 138

A2.3 Luminosity distance 138

A2.4 Angular diameter distance 143

A2.5 Source counts 145

Advanced Topic 3 Neutrino Cosmology 149

A3.1 The massless case 149

A3.2 Massive neutrinos 151

A3.2.1 Light neutrinos 152

A3.2.2 Heavy neutrinos 153

A.3 Neutrinos and structure formation 153

Advanced Topic 4 Baryogenesis 157

Advanced Topic 5 Structures in the Universe 161

A5.1 The observed structures 161

A5.2 Gravitational instability 163

A5.3 The clustering of galaxies 165

A5.4 Cosmic microwave background anisotropies 167

A5.4.1 Statistical description of anisotropies 167

A5.4.2 computing the c l 169

A5.4.3 Microwave background observations 171

A5.4.4 Spatial geometry 172

A5.5 The origin of structure 173

Advanced Topic 6 Constraining Cosmological Models 177

A6.1 Cosmological models and parameters 177

A6.2 Key cosmological observations 178

A6.3 Cosmological data analysis 179

A6.4 The Standard Cosmological Model: 2025 edition 181

A6.5 Tensions and hints of new physics 184

A6.6 The future 185

Bibliography 187

Numerical Answers and Hints to Problems 191

Index 197

An Introduction to Modern Cosmology