First Principles of Cosmology

by Eric V. Linder

Table of Contents

PART 1. OVERVIEW

Chapter 1. Preliminaries

1.1 Vital Statistics
1.2 Units
1.3 Equivalence Principle
1.4 Metric
1.5 Homogeneity and Isotropy
1.6 Energy-Momentum Tensor

Chapter 2. Dynamics of the Universe

2.1 Friedmann Equations
2.2 History of Modern Cosmology
2.3 Equation of State
2.4 Density Evolution
2.5 Time Evolution
2.6 Fate of the Universe

Chapter 3. Cosmological Models

3.1 Cosmological Parameters
3.2 Classical Cosmological Tests
3.2.1 Lookback Time / Age Test
3.2.2 Distance Tests
3.2.3 Magnitude Test
3.2.4 Volume Test
3.2.5 Number Test
3.3 Discrimination of Models
3.3.1 Low Redshift
3.3.2 Moderate Redshift
3.3.3 Evolution
3.3.4 High Redshift
3.4 Summary of Classical Cosmological Tests
3.5 Other Cosmological Tests
3.5.1 Surface Brightness Fluctuations
3.5.2 Time Dependent Redshift
3.5.3 Period Test
3.6 Clumpy Universe Distances

Chapter 4. History of the Universe

4.1 Scaling
4.2 Temperature-Time-Redshift Relation
4.3 History In Brief
4.4 Planck Era
4.5 Baryogenesis
4.6 Neutrino Background
4.7 Inflation
4.7.1 Physics
4.7.2 Horizons
4.7.3 Flatness

PART 2. THREE CORNERSTONES

Chapter 5. Hubble Expansion

5.1 Observations
5.2 General Theory
5.2.1 Doppler Shift
5.2.2 Expansion Shift
5.2.3 General Expression
5.2.4 Four Observed Properties
5.2.5 Hubble Constant
5.3 Redshift Tests
5.3.1 Microwave Background Temperature
5.3.2 Surface Brightness
5.3.3 Olbers' Paradox
5.4 Alternate Theories
5.4.1 Doppler Shift
5.4.2 Tired Light
5.4.3 Photon Mass
5.4.4 Wolf Shift
5.4.5 Gravitational Shift
5.4.6 Summary

Chapter 6. Nucleosynthesis

6.1 Introduction
6.2 Thermodynamics
6.2.1 Thermal History
6.2.2 Interaction Equilibrium
6.2.3 Temperature-Time Relation Redux
6.2.4 Breakdown of Equilibrium
6.2.5 Entropy
6.3 Calculating Abundances
6.3.1 Helium Heuristically
6.3.2 Reaction Networks
6.3.3 Approximate Integration
6.3.4 Quasistatic Analysis
6.4 Observing Abundances
6.5 Inhomogeneous Nucleosynthesis
6.6 Constraints from Nucleosynthesis
6.6.1 Baryon Density
6.6.2 Neutrino Species
6.6.3 Component Densities
6.6.4 Varying Gravitation
6.6.5 Microwave Background Temperature

Chapter 7. Cosmic Microwave Background Radiation

7.1 Introduction
7.2 Recombination Physics
7.2.1 Recombination
7.2.2 Decoupling
7.2.3 Last Scattering Surface
7.3 Spectrum
7.3.1 Formation
7.3.2 Planck Function
7.4 Distortions
7.4.1 Bose-Einstein Distortion
7.4.2 Lines
7.4.3 Comptonization
7.5 Anisotropy Properties
7.5.1 Angular Scales
7.5.2 Correlation Function
7.5.3 Decompostion
7.5.4 Observations
7.6 Anisotropy Mechanisms
7.6.1 Dipole
7.6.2 Sachs-Wolfe Effect
7.6.3 Perturbations
7.6.4 Sunyaev-Zel'dovich Effect
7.6.5 Reionization
7.7 Early Universe Constraints
7.7.1 Gravitational Waves
7.7.2 Cosmic Strings
7.7.3 Inflation
7.8 Recent Universe Constraints
7.8.1 Cosmic Rays
7.8.2 Hubble Constant

PART 3. STRUCTURE

Chapter 8. Structure Formation

8.1 Linear Perturbation Theory
8.1.1 Newtonian and FRW Analogies
8.1.2 Perturbation Equations
8.1.3 Perturbation Solutions
8.2 Statistical Measures
8.2.1 N-point Correlations
8.2.2 Power Spectrum
8.2.3 Thermodynamic Function
8.3 Clustering
8.3.1 Zel'dovich Approximation
8.3.2 Adhesion Model
8.3.3 Environmental Effects
8.3.4 Biasing
8.4 Large Scale Flows
8.4.1 Peculiar Velocities
8.4.2 Dipole Alignment
8.5 Radiation Effects
8.5.1 Radiation Damping
8.5.2 Radiation Instability
8.5.3 Sachs-Wolfe Effect

Beyond the Horizon