An Introduction to Modern Cosmology

An Introduction to Modern Cosmology Third Edition is an accessible account of modern cosmological ideas. The Big Bang Cosmology is explored, looking at its observational successes in explaining the expansion of the Universe, the existence and properties of the cosmic microwave background, and the origin of light elements in the universe. Properties of the very early Universe are also covered, including the motivation for a rapid period of expansion known as cosmological inflation. The third edition brings this established undergraduate textbook up-to-date with the rapidly evolving observational situation.

This fully revised edition of a bestseller takes an approach which is grounded in physics with a logical flow of chapters leading the reader from basic ideas of the expansion described by the Friedman equations to some of the more advanced ideas about the early universe. It also incorporates up-to-date results from the Planck mission, which imaged the anisotropies of the Cosmic Microwave Background radiation over the whole sky. The Advanced Topic sections present subjects with more detailed mathematical approaches to give greater depth to discussions. Student problems with hints for solving them and numerical answers are embedded in the chapters to facilitate the reader’s understanding and learning.

Cosmology is now part of the core in many degree programs. This current, clear and concise introductory text is relevant to a wide range of astronomy programs worldwide and is essential reading for undergraduates and Masters students, as well as anyone starting research in cosmology.

The accompanying website for this text, http://booksupport.wiley.com, provides additional material designed to enhance your learning, as well as errata within the text. 

Andrew Liddle
Institute for Astronomy, University of Edinburgh, UK

Preface xi

Constants, conversion factors and symbols xiv

1 A (Very) Brief History of Cosmological Ideas 1

2 Observational Overview 3

2.1 In visible light 3

2.2 In other wavebands 6

2.3 Homogeneity and isotropy 10

2.4 The expansion of the Universe 10

2.5 Particles in the Universe 13

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 c2 28

4 The Geometry of the Universe 29

4.1 Flat geometry 29

4.2 Spherical geometry 30

4.3 Hyperbolic geometry 32

4.4 Infinite and observable Universes 33

4.5 Where did the Big Bang happen? 33

4.6 Three values of k 34

5 Simple Cosmological Models 37

5.1 Hubble’s law 37

5.2 Expansion and redshift 38

5.3 Solving the equations 39

5.4 Particle number densities 43

5.5 Evolution including curvature 44

6 Observational Parameters 49

6.1 The expansion rate H0 49

6.2 The density parameter 0 51

6.3 The deceleration parameter q0 52

7 The Cosmological Constant 55

7.1 Introducing _ 55

7.2 Fluid description of _ 56

7.3 Cosmological models with _ 57

8 The Age of the Universe 61

9 The Density of the Universe and Dark Matter 67

9.1 Weighing the Universe 67

9.2 What might the dark matter be?  73

9.3 Dark matter searches 74

10 The Cosmic Microwave Background 77

10.1 Properties of the microwave background 77

10.2 The photon to baryon ratio 79

10.3 The origin of the microwave background 80

10.4 The origin of the microwave background (advanced) 83

11 The Early Universe 87

12 Nucleosynthesis: The Origin of the Light Elements 93

12.1 Hydrogen and Helium 93

12.2 Comparing with observations 96

12.3 Contrasting decoupling and nucleosynthesis 98

13 The Inflationary Universe 101

13.1 Problems with the Hot Big Bang 101

13.2 Inflationary expansion 105

13.3 Solving the Big Bang problems 106

13.4 How much inflation? 108

13.5 Inflation and particle physics 109

14 The Initial Singularity 113

15 Overview: The Standard Cosmological Model 117

Advanced Topic 1 General Relativistic Cosmology 121

1.1 The metric of space-time 121

1.2 The Einstein equations 122

1.3 Aside: Topology of the Universe 124

Advanced Topic 2 Classic Cosmology: Distances and Luminosities 127

2.1 Light propagation and redshift 127

2.2 The observable Universe 130

2.3 Luminosity distance 130

2.4 Angular diameter distance 134

2.5 Source counts 136

Advanced Topic 3 Neutrino Cosmology 139

3.1 The massless case 139

3.2 Massive neutrinos 141

3.3 Neutrinos and structure formation 142

Advanced Topic 4 Baryogenesis 145

Advanced Topic 5 Structures in the Universe 149

5.1 The observed structures 149

5.2 Gravitational instability 151

5.3 The clustering of galaxies 152

5.4 Cosmic microwave background anisotropies 154

5.5 The origin of structure 159

Advanced Topic 6 Constraining cosmological models 163

6.1 Cosmological models and parameters 163

6.2 Key cosmological observations 164

6.3 Cosmological data analysis 164

6.4 The Standard Cosmological Model: 2014 edition 166

6.5 The future 168

Bibliography 171

Numerical answers and hints to problems 173

Index 177

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