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An Introduction to Modern Cosmology
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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

About the Author

Andrew Liddle Institute for Astronomy, University of Edinburgh, UK

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