PERTURBATION-THEORY BASED ON THE EINSTEIN-BOLTZMANN SYSTEM .2. ILLUSTRATION OF THE THEORY FOR AN ALMOST-ROBERTSON-WALKER GEOMETRY

This is the second in a pair of articles, the overall objective of whi ch is to describe within the framework of the Einstein-Boltzmann syste m a self-consistent perturbation method which leads to a tractable set of integrodifferential equations for the rate of change of the metric and the distribution function. The main purpose here is to prove that , for cases where the pressure of the gas of massive particles vanishe s in the background, the treatment of the Einstein-Boltzmann system by means of a suitable perturbation method automatically produces a comp lete scheme of hydro-dynamics, consisting of a closed set of partial d ifferential equations for the evaluation of the mean velocity, the mas s density, the temperature or the pressure, and the metric. The growin g hydrodynamic modes are systematically derived for an almost-Robertso n-Walker universe model, and the calculations are proposed without mak ing any restrictions on the form of the perturbed metric. To summarize , the present article suggests a scheme of hydrodynamics for the late stages of cosmic expansion and calls attention to the support and inte rpretation given by the general-relativistic kinetic theory of monatom ic gases to this scheme. Comparison with the predictions of the Eckart and/or Landau-Lifshitz theories of dissipative fluids is also briefly presented.