Fluid and gas models in FLRW and almost FLRW universes

Abstract

Recently the universe has been modeled in the covariant sense, in terms of fluid models and perturbations thereof, leading to Gauge Invariant Covariant (GIC) perturbations of these fluid models. It is well known that kinetic theory provides a physically sound and consistent description of the matter and radiation in the universe, so a perturbative theory of gas models using kinetic theory would be most helpful. This has been done to a large degree in the Gauge Invariant (GI) Bardeen approach to perturbation theory by studies of gases based on the relativistic Boltzmann equation. These treatments, however, were not fully covariant. The GI Bardeen approach is dependent on a co-ordinate choice, while in the full GIC perturbation theory full covariance is maintained along with gauge invariance by describing the theory in a particular set of perturbation variables that differ from the Bardeen choice but can be related to the Bardeen variables. The covariant formulation of the relativistic Boltzmann equation in terms of variables that are of use in the GIC theory for gases has been well described. In this thesis, I provide both a good introduction to the full GIC perturbation theory of a photon gas and matter fluid system in the linear theory as well as a solid grounding with respect to the exact FLRW fluid model upon which most of the original ideas and concepts of modern cosmology are based. The introduction to the exact FLRW model is done in the sense of the dynamical systems approach to cosmology which provides the easiest access to understanding the evolution of single and multi-fluid FLRW models.