Modern cosmology

Description

Contents About the authors Preface 1 The concordance model of cosmology 1.1 A nutshell history of the universe 1.2 The Hubble diagram 1.3 Big Bang nucleosynthesis 1.4 The cosmic microwave background 1.5 Structure in the universe 1.6 ΛCDM: the concordance model of cosmology 1.7 Summary and outlook Exercises 2 The expanding universe 2.1 Expanding space 2.1.1 The metric 2.1.2 The geodesic equation 2.2 Distances 2.3 Evolution of energy 2.4 Cosmic inventory 2.4.1 Photons 2.4.2 Baryons 2.4.3 Dark matter 2.4.4 Neutrinos 2.4.5 Epoch of matter-radiation equality 2.4.6 Dark energy 2.5 Summary Exercises 3 The fundamental equations of cosmology 3.1 Einstein equations 3.2 Boltzmann equation 3.2.1 Boltzmann equation for particles in a harmonic potential 3.2.2 Boltzmann equation in an expanding universe 3.2.3 Collision terms 3.3 Beyond the homogeneous universe 3.3.1 Perturbed spacetime 3.3.2 The geodesic equation 3.3.3 The collisionless Boltzmann equation for radiation 3.3.4 The collisionless Boltzmann equation for massive particles 3.4 Summary Exercises 4 The origin of species 4.1 The homogeneous Boltzmann equation revisited 4.2 Big Bang nucleosynthesis 4.2.1 Neutron abundance 4.2.2 Light element abundances 4.3 Recombination 4.4 Dark matter 4.5 Summary Exercises 5 The inhomogeneous universe: matter & radiation 5.1 The collisionless Boltzmann equation for photons 5.2 Collision terms: Compton scattering 5.3 The Boltzmann equation for photons 5.4 The Boltzmann equation for cold dark matter 5.5 The Boltzmann equation for baryons 5.6 The Boltzmann equation for neutrinos 5.7 Summary Exercises 6 The inhomogeneous universe: gravity 6.1 Scalar-vector-tensor decomposition 6.2 From gauge to gauge 6.3 The Einstein equations for scalar perturbations 6.3.1 Ricci tensor 6.3.2 Two components of the Einstein equations 6.4 Tensor perturbations 6.4.1 Christoffel symbol for tensor perturbations 6.4.2 Ricci tensor for tensor perturbations 6.4.3 Einstein equations for tensor perturbations 6.4.4 Verifying the decomposition theorem 6.5 Summary Exercises 7 Initial conditions 7.1 The horizon problem and a solution 7.2 Inflation 7.3 Gravitational wave production 7.3.1 Quantizing the harmonic oscillator 7.3.2 Tensor perturbations 7.4 Scalar perturbations 7.4.1 Scalar field perturbations around an unperturbed background 7.4.2 Super-horizon perturbations 7.4.3 Spatially flat slicing 7.5 The Einstein-Boltzmann equations at early times 7.6 Summary Exercises 8 Growth of structure: linear theory 8.1 Prelude 8.1.1 Three stages of evolution 8.1.2 Closing the Boltzmann hierarchy 8.2 Large scales 8.2.1 Super-horizon solution 8.2.2 Through horizon crossing 8.3 Small scales 8.3.1 Horizon crossing 8.3.2 Sub-horizon evolution 8.4 The transfer function 8.5 The growth factor 8.6 Beyond cold dark matter and radiation 8.6.1 Baryons 8.6.2 Massive neutrinos 8.6.3 Dark energy 8.7 Summary Exercises 9 The cosmic microwave background 9.1 Overview 9.2 Large-scale anisotropies 9.3 Acoustic oscillations 9.3.1 Tightly-coupled limit of the Boltzmann equations 9.3.2 Tightly-coupled solutions 9.4 Diffusion damping 9.5 Inhomogeneities to anisotropies 9.5.1 Free streaming 9.5.2 The angular power spectrum 9.6 The CMB power spectrum 9.6.1 Large angular scales 9.6.2 Acoustic peaks 9.7 Cosmological parameters 9.7.1 Curvature and Λ 9.7.2 Amplitude, spectral index, and optical depth 9.7.3 Baryon and CDM densities 9.8 Summary Exercises 10 The polarized CMB 10.1 Polarization 10.2 Generating polarization from Compton scattering 10.3 Polarization from a single plane wave 10.4 Boltzmann solution 10.5 Polarization power spectra 10.6 Detecting gravitational waves 10.7 Summary Exercises 11 Probes of structure: tracers 11.1 Galaxy clustering 11.1.1 Galaxy statistics 11.1.2 Redshift-space distortions 11.1.3 BAO and Alcock-Paczyński 11.2 Angular correlations 11.3 The Sunyaev-Zel'dovich effect 11.4 Summary Exercises 12 Growth of structure: beyond linear theory 12.1 Prelude 12.2 Perturbation theory 12.3 Simulations 12.4 Dark matter halos 12.4.1 Halo masses and profiles 12.4.2 The halo mass function 12.5 Galaxy clusters 12.6 Galaxy clustering and bias 12.7 The halo model 12.8 Summary Exercises 13 Probes of structure: lensing 13.1 Overview 13.2 Photon geodesics 13.3 CMB lensing 13.4 Galaxy shapes 13.5 Weak-lensing statistics 13.5.1 Shear power spectrum 13.5.2 Shear correlation function 13.5.3 Shear cross-correlations 13.6 Summary Exercises 14 Analysis and inference 14.1 The likelihood function 14.2 Overview: from raw data to parameter constraints 14.3 Mapmaking 14.4 Two-point functions 14.4.1 CMB power spectrum 14.4.2 Galaxy power spectrum 14.5 The Fisher matrix 14.6 Sampling the likelihood function 14.7 Summary Exercises A Solutions to selected exercises Chapter 1 Exercise 1.1 Exercise 1.2 Exercise 1.4 Chapter 2 Exercise 2.1 Exercise 2.4 Exercise 2.5 Exercise 2.7 Exercise 2.8 Exercise 2.11 Chapter 3 Exercise 3.2 Exercise 3.6 Exercise 3.7 Exercise 3.8 Exercise 3.12 Chapter 4 Exercise 4.1 Exercise 4.6 Exercise 4.9 Chapter 5 Exercise 5.3 Exercise 5.4 Chapter 6 Exercise 6.1 Exercise 6.3 Exercise 6.8 Chapter 7 Exercise 7.2 Exercise 7.12 Exercise 7.13 Chapter 8 Exercise 8.4 Exercise 8.8 Exercise 8.13 Chapter 9 Exercise 9.2 Exercise 9.9 Exercise 9.16 Exercise 9.17 Chapter 10 Exercise 10.1 Exercise 10.6 Chapter 11 Exercise 11.1 Exercise 11.4 Exercise 11.8 Chapter 12 Exercise 12.4 Exercise 12.10 Exercise 12.13 Chapter 13 Exercise 13.1 Exercise 13.4 Chapter 14 Exercise 14.4 Exercise 14.10 B Numbers B.1 Physical constants B.2 Astrophysical constants B.3 Fiducial cosmology C Special functions C.1 Legendre polynomials C.2 Spherical harmonics C.3 Spherical Bessel functions C.4 Fourier transforms C.5 Miscellaneous D Symbols D.1 Mathematical and geometrical definitions D.2 Frequently used relations D.3 Symbol definitions Bibliography Index