PERTURBATION-THEORY BASED ON THE EINSTEIN-BOLTZMANN SYSTEM .1. ILLUSTRATION OF THE THEORY FOR A ROBERTSON-WALKER GEOMETRY

This article is a discussion of how it is possible to do perturbation theory for the Einstein-Boltzmann system about a dust solution. Explic itly expressed, the background Robertson-Walker universe model and one -parameter families of exact solutions are applied to the Einstein-Bol tzmann system to obtain a closed-form solution of the equations govern ing linearized perturbations at late times, when the nonzero pressure of the gas of massive particles may be regarded as being significantly smaller than the energy density. After splitting the distribution fun ction into two structurally different parts, the analysis given here p rovides a means of deriving the equations of linear hydrodynamics. In fact, due to the specific properties of the background chosen, one can prove that the evolution of suitably defined hydrodynamic variables i s exactly decoupled from the evolution of the phase-space function sat isfying the linearized Boltzmann equation. For simplicity, the working s of the method are illustrated by assuming that the perturbed metric is also of the Robertson-Walker form. A detailed treatment of the effe ct of inhomogeneities in an almost-Robertson-Walker universe model wil l be the subject of the last article in this series.