There are two aspects of cosmology today that make it more alluring than ever. First, there is an enormous amount of data. To give just one example of how rapidly our knowledge of the structure of the universe is advancing, consider galaxy surveys which map the sky. In 1985, the state-of-the-art survey was the one carried out by the Center for Astrophysics; it consisted of the positions of 1100 galaxies. Today, the Sloan Digital Sky Survey and the Two Degree Field between them have recorded the 3D positions of half a million galaxies.

1 The Standard Model and Beyond

 1.1 The Expanding Universe

 1.2 The Hubble Diagram

 1.3 Big Bang Nucleosynthesis

 1.4 The Cosmic Microwave Background

 1.5 Beyond the Standard Model

 1.6 Summary

 Exercises

2 The Smooth, Expanding Universe

 2.1 General Relativity

2.1.1 The Metric

2.1.2 The Geodesic Equation

2.1.3 Einstein Equations

 2.2 Distances

 2.3 Evolution of Energy

 2.4 Cosmic Inventory

2.4.1 Photons

2.4.2 Baryons

2.4.3 Matter

2.4.4 Neutrinos

2.4.5 Dark Energy

2.4.6 Epoch of Matter-Radiation Equality

 2.5 Summary

 Exercises

3 Beyond Equilibrium

 3.1 Boltzmann Equation for Annihilation

 3.2 Big Bang Nucleosynthesis

3.2.1 Neutron Abundance

3.2.2 Light Element Abundances

 3.3 Recombination

 3.4 Dark Matter

 3.5 Summary

 Exercises

4 The Boltzmann Equations

 4.1 The Boltzmann Equation for the Harmonic Oscillator

 4.2 The Collisionless Boltzmann Equation for Photons

4.2.1 Zero-Order Equation

4.2.2 First-Order Equation

 4.3 Collision Terms: Compton Scattering

 4.4 The Boltzmann EqUation for Photons

 4.5 The Boltzmann Equation for Cold Dark Matter

 4.6 The Boltzmann Equation for Baryons

 4.7 Summary

 Exercises

 Einstein Equations

 5.1 The Perturbed Ricci Tensor and Scalar

5.1.1 Christoffel Symbols

5.1.2 Ricci Tensor

 5.2 Two Components of the Einstein Equations

 5.3 Tensor Perturbations

5.3.1 Christoffel Symbols for Tensor Perturbations

5.3.2 Ricci Tensor for Tensor Perturbations

5.3.3 Einstein Equations for Tensor Perturbations

 5.4 The Decomposition Theorem

 5.5 From Gauge to Gauge

 5.6 Summary

 Exercises

 Initial Conditions

 6.1 The Einstein-Boltzmann Equations at Early Times

 6.2 The Horizon

 6.3 Inflation

6.3.1 A Solution to the Horizon Problem

6.3.2 Negative Pressure

6.3.3 Implementation with a Scalar Field

 6.4 Gravity Wave Production

6.4.1 Quantizing the Harmonic Oscillator

6.4.2 Tensor Perturbations

  6.5 Scalar Perturbations

6.5.1 Scalar Field Perturbations around a Smooth Background

6.5.2 Super-Horizon Perturbations

6.5.3 Spatially Flat Slicing

 6.6 Summary and Spectral Indices

 Exercises

 Inhomogeneities

 7.1 Prelude

7.1.1 Three Stages of Evolution

7.1.2 Method

 7.2 Large Scales

7.2.1 Super-horizon Solution

7.2.2 Through Horizon Crossing

 7.3 Small Scales

7.3.1 Horizon Crossing

7.3.2 Sub-horizon Evolution

 7.4 Numerical Results and Fits

 7.5 Growth Function

 7.6 Beyond Cold Dark Matter

7.6.1 Baryons

7.6.2 Massive Neutrinos

7.6.3 Dark Energy

 Exercises

8 Anisotropies

 8.1 Overview

 8.2 Large-Scale Anisotropies

 8.3 Acoustic Oscillations

8.3.1 Tightly Coupled Limit of the Boltzmann Equations

8.3.2 Tightly Coupled Solutions

 8.4 Diffusion Damping

 8.5 Inhomogeneities to Anisotropies

8.5.1 Free Streaming

8.5.2 The Cl's

 8.6 The Anisotropy Spectrum Today

8.6.1 Sachs-Wolfe Effect

8.6.2 Small Scales

 8.7 Cosmological Parameters

8.7.1 Curvature

8.7.2 Degenerate Parameters

8.7.3 Distinct Imprints

 Exercises

9 Probes of Inhomogeneities

 9.1 Angular Correlations

 9.2 Peculiar Velocities

 9.3 Direct Measurements of Peculiar Velocities

 9.4 Redshift Space Distortions

 9.5 Galaxy Clusters

 Exercises

10 Weak Lensing and Polarization

 10.1 Gravitational Distortion of Images

 10.2 GeodesiCs and Shear

 10.3 Ellipticity as an Estimator of Shear

 10.4 Weak Lensing Power Spectrum

 10.5 Polarization: The Quadrupole and the Q/U DecompositioI

 10.6 Polarization from a Single Plane Wave

 10.7 Boltzmann Solution

 10.8 Polarization Power Spectra

 10.9 Detecting Gravity Waves

 Exercises

11 Analysis

 11.1 The Likelihood Function

11.1.1 Simple Example

11.1.2 CMB Likelihood

11.1.3 Galaxy Surveys

 11.2 Signal Covariance Matrix

11.2.1 CMB Window Functions

11.2.2 Examples of CMB Window Functions

11.2.3 Window Functions for Galaxy Surveys

11.2.4 Summary

 11.3 Estimating the Likelihood Function

11.3.1 Karhunen-Loeve Techniques

11.3.2 Optimal Quadratic Estimator

 11.4 The Fisher Matrix: Limits and Applications

11.4.1 CMB

11.4.2 Galaxy Surveys

11.4.3 Forecasting

 11.5 Mapmaking and Inversion

 11.6 Systematics

11.6.1 Foregrounds

11.6.2 Mode Subtraction

 Exercises

A Solutions to Selected Problems

B Numbers

 B.1 Physical Constants

 B.2 Cosmological Constants

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

Bibliography

Index