Dynamics of early & late universe cosmology - Emond, William (2018)
In this thesis we discuss two key problems: the cosmological constant problem (CCP), an issue that primarily manifests itself in late universe cosmology; and the process of thermalisation during the post-inflationary reheating phase of the early universe. We start by giving a brief review of general relativity, discussing both its successes and failures, in particular, why one might consider modifications of it. We then delve into the aspects of early and late universe cosmology that we aim to address in the research discussed in this thesis. Starting with an overview of the inflationary paradigm, and the need to reheat the universe post-inflation, we give a review of previous research that has been conducted in this area. We then move on to discuss the CCP in detail, in particular, why it is such an issue. After setting the scene for this problem, we proceed to discuss how to approach finding a resolution to it, highlighting certain stumbling blocks that one needs to be mindful of. Having set the scene, we then present a potential solution to the CCP, involving a scalar-tensor modifed theory of gravity, so-called Horndeski theory. Building upon a class of Horndeski theories providing self-tuning solutions to the CCP, we provide a generalisation in which matter interacts with gravity via a disformal coupling to the spacetime metric. We establish the form of the disformally self-tuning Lagrangian on a cosmological Friedmann-Robertson-Walker background, and show that there exist non-trivial self-tuning solutions. In the latter half of this thesis, we move on to review the literature on the non-perturbative description of the early stages of reheating, so-called preheating. With the motivation to study the less well understood thermalisation process that must necessarily take place in this phase, we then present a toy model preheating theory, in which we account for the effects of thermalisation from its onset. Within the density matrix formalism, we derive a (self-consistent) set of quantum Boltzmann equations, which are able to describe the evolution of an ensemble of self-interacting scalar particles that are subject to an oscillating mass term. In particular, we apply this to the preheating scenario in order to study the evolution of scalar particle number densities throughout this process. We then conclude by discussing our numerical analysis of the Boltzmann equations, drawing attention to some important results and features that manifest using this approach, in particular, how the process differs from the standard analysis through the inclusion of thermalisation.