Lecture notes based on the lectures on cosmological
dynamics given by E. Bertschinger at Les Houches in August 1993

astro-ph/9503125

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**Table of Contents**

- PREFACE
- ELEMENTARY MECHANICS
- Newtonian dynamics in cosmology
- Lagrangian and Hamiltonian formulations
- Conservation of momentum and energy?

- EULERIAN FLUID DYNAMICS
- Cosmological fluid equations
- Linear instability 1: isentropic fluctuations and Jeans criterion
- Linear instability 2: entropy fluctuations and isocurvature mode
- Vorticity - or potential flow?

- HOT DARK MATTER
- Tremaine-Gunn bound
- Vlasov equation
- Nonrelativistic evolution in an external gravitational field
- Nonrelativistic evolution including self-gravity

- RELATIVISTIC COSMOLOGICAL PERTURBATION THEORY
- Introduction
- Synopsis
- Summary of essential relativity

- Classification of metric perturbations
- Stress-energy tensor
- Synchronous gauge
- Gauge modes
- Poisson gauge
- Physical content of the Einstein equations
- Hamiltonian dynamics of particles
- Lagrangian field equations

- Introduction
- REFERENCES