Peculiar velocity flows, kinetic theory and large-scale structure

Peculiar velocity flows in a perturbed Robertson -Walker universe are considered. The dependence of these velocities on the density parameter, Omega _0, is found for two cases: (1) adiabatic perturbations and (2) fixed attractors. The case of adiabatic perturbations is found to agree with Peebles' results, while the case of fixed attractors gives a somewhat different Omega_0 dependence. Kinetic theory is used to provide a better method of defining the equation of state. For a collisionless system, the distribution function and the equation of state are found for the pure Robertson-Walker case as a function of the parameter beta, which is a measure of the average magnitude of the peculiar flow of the test particles. The effects of these peculiar flows on the expansion parameter and on observed redshifts are calculated. The basic equations for kinetic theory in the perturbed Robertson-Walker case are found, and although no analytical solutions are found, Rasio, Shapiro, and Teukolsky's approach for numerical solution is discussed. Also, integral relations for certain moments of the perturbed distribution function are found from the Einstein equation.