IoP. An Introduction to the Science of Cosmology. Derek Raine. Ted Thomas. Series in Astronomy and Astrophysics

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1 Series in Astronomy and Astrophysics An Introduction to the Science of Cosmology Derek Raine Department of Physics and Astronomy University of Leicester, UK Ted Thomas Department of Physics and Astronomy University of Leicester, UK IoP Institute of Physics Publishing Bristol and Philadelphia

2 Preface 1 Reconstructing time 1.1 The patterns of the stars 1.2 Structural relics 1.3 Material relics 1.4 Ethereal relics 1.5 Cosmological principles 1.6 Theories 1.7 Problems 2 Expansion 2.1 The redshift 2.2 The expanding Universe 2.3 The distance scale 2.4 The Hubble constant 2.5 The deceleration parameter 2.6 The age of the Universe 2.7 The steady-state theory 2.8 The evolving Universe 2.9 Problems 3 Matter The mean mass density of the Universe The critical density The density parameter Contributions to the density Determining the matter density The mean luminosity density Comoving volume Luminosity function Luminosity density The mass-to-luminosity ratios of galaxies Rotation curves 26 xi

3 vi Elliptical galaxies The virial theorem The mass-to-luminosity ratios of rich clusters Virial masses of clusters Baryonic matter Intracluster gas The gravitational lensing method The intercluster medium The non-baryonic dark matter Dark matter candidates Massive neutrinos? 34 ' * '* Axions? Neutralinos? The search for WIMPS Antimatter Appendix. Derivation of the virial theorem Problems 39 4 Radiation Sources of background radiation The radio background Infrared background, Optical background Other backgrounds The microwave background Isotropy The hot big bang The cosmic radiation background in the steady-state theory Radiation and expansion Redshift and expansion Evolution of the Planck spectrum Evolution of energy density Entropy of radiation Nevertheless it moves Measurements of motion The x-ray background Problems 5 Relativity 5.1 Introduction 5.2 Space geometry 5.3 Relativistic geometry The principle of equivalence Physical relativity 5.4 Isotropic and homogeneous geometry

4 vii Homogeneity of the 2-sphere Homogeneity of the metric Uniqueness of the space metric Uniqueness of the spacetime metric Other forms of the metric A radial coordinate related to area A radial coordinate related to proper distance Open and closed spaces Fundamental (or comoving) observers Redshift The velocity-distance law A Time dilation 5.11 The field equations Equations of state The cosmological constant The critical density The dust Universe Evolution of the density parameter Evolution of the Hubble parameter The relationship between redshift and time Newtonian interpretation Explicit solutions p = 0, k = 0, A = 0, the Einstein-de Sitter model The case/? = 0, k =+1, A = The case p = 0, k =-1, A = Models with a cosmological constant Negative A Positive A Positive A and critical density The case A > 0, k = ' 5.16 The radiation Universe \ The relation between temperature and time Light propagation in an expanding Universe The Hubble sphere The particle horizon Alternative equations of state Problems 97 Models The classical tests, The Mattig relation The case p = 0, A = The general case p = 0, A The angular diameter-redshift test 104

5 viii Theory Observations 6.4 The apparent magnitude-redshift test Theory The K-correction Magnitude versus redshift: observations 6.5 The geometry of number counts: theory Number counts: observations The galaxy number-magnitude test 6.6 The timescale test The ages of the oldest stars 6.7 The lensed quasar test 6.8 Problems with big-bang cosmology The horizon problem The flatness problem The age problem The singularity problem 6.9 Alternative cosmologies 6.10 Problems 7 Hot big bang 7.1 Introduction 7.2 Equilibrium thermodynamics Evolution of temperature: relativistic particles Evolution of temperature: non-relativistic particles 7.3 The plasma Universe 7.4 The matter era 7.5 The radiation era Temperature and time Timescales: the Gamow criterion 7.6 The era of equilibrium 7.7 The GUT era: baryogenesis The strong interaction era The weak interaction era: neutrinos Entropy and e~ e + pair annihilation 7.8 Photon-to-baryon ratio 7.9 Nucleosynthesis Weak interactions: neutron freeze-out Helium Light elements Abundances and cosmology 7.10 The plasma era Thomson scattering Free-free absorption

6 ix Compton scattering 7.11 Decoupling 7.12 Recombination 7.13 Last scattering 7.14 Perturbations 7.15 Appendix A. Thermal distributions Chemical potentials Photon energy density Photon number density Relativistic neutrinos Relativistic electrons Entropy densities 7.16 Appendix B. The Saha equation 7.17 Appendix C. Constancy of r\ 7.18 Problems Inflation 8.1 The horizon problem 8.2 The flatness problem 8.3 Origin of structure 8.4 Mechanisms, Equation of motion for the inflaton field Equation of state Slow roll 8.5 Fluctuations 8.6 Starting inflation 8.7 Stopping inflation Particle physics and inflation 8.8 Topological defects 8.9 Problems Structure 9.1 The problem of structure 9.2 Observations The edge of the Universe 9.3 Surveys and catalogues 9.4 Large-scale structures 9.5 Correlations Correlation functions Linear distribution The angular correlation function Results 9.6 Bias 9.7 Growth of perturbations Static background, zero pressure

7 x Expanding background The Jeans'mass Adiabatic perturbations Isocurvature (isothermal) perturbations Superhorizon size perturbations Dissipation The spectrum of fluctuations Structure formation in baryonic models Dark matter models Growth of fluctuations in dark matter models Observations of the microwave background Appendix A Appendix B Problems Epilogue Homogeneous anisotropy Kasner solution Growing modes The rotating Universe The arrow of time 208 Reference material < 210 Constants 210 Useful quantities 210 Formulae 211 Symbols 212 References 213 Index 217

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