Cosmological models (Carg\`{e}se lectures 1998)

TL;DR

This set of lectures systematically presents the 1+3 covariant approach to relativistic cosmological models, covering geometric, dynamical, observational aspects, and perturbation theory, with applications to exact models and symmetries.

Contribution

It provides a comprehensive, systematic presentation of the 1+3 covariant formalism, including new tetrad equations, classification of models, and gauge-invariant perturbation theory.

Findings

Derivation of full set of tetrad equations

Classification of cosmological models with symmetries

Introduction to gauge-invariant perturbation theory

Abstract

The aim of this set of lectures is a systematic presentation of a 1+3 covariant approach to studying the geometry, dynamics, and observational properties of relativistic cosmological models. In giving (i) the basic 1+3 covariant relations for a cosmological fluid, the present lectures cover some of the same ground as a previous set of Carg\`{e}se lectures \cite{ell73}, but they then go on to give (ii) the full set of corresponding tetrad equations, (iii) a classification of cosmological models with exact symmetries, (iv) a brief discussion of some of the most useful exact models and their observational properties, and (v) an introduction to the gauge-invariant and 1+3 covariant perturbation theory of almost-Friedmann-Lema\^{\i}tre-Robertson-Walker universes, with a fluid description for the matter and a kinetic theory description of the radiation.