Modern Cosmology

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