Relaxation-time approximation for a Boltzmann gas in Robertson-Walker universe models

Abstract

Given Einstein's theory of gravitation, the relaxation-time approximation for a general-relativistic Boltzmann equation is studied with a view to demonstrating its usefulness in the context of Robertson-Walker universe models. Solutions of the full nonlinear equations for the metric and the distribution function are examined, together with their relation to linearized perturbations. Emphasis is placed on finding analogs of the exact results on strong or weak convergence to equilibrium employed in special-relativistic kinetic theory. At the late stages of cosmic expansion, an explicit choice of the empirical collision frequency is made to fit optimally the relaxation-time model to the “actual” Einstein-Boltzmann system. Finally, perspectives for some future generalizations are outlined.