Phase planes in the universe : chaotic cyclic universes and kicking Chameleons - Platts, Emma (Department of Mathematics and Applied Mathematics, 2016)
This thesis consists of two main sections: chaotic cyclic cosmology and Chameleon gravity in the early universe. Both sections invoke a phase plane analysis as their commonality. The first explores a cyclic model, proposed by Ellis et al, that is in keeping with current observations. No exotic nor new physics is needed for the bounce nor the turnaround. The model is chaotic in nature and requires only that the universe is closed and that dark energy (at some time) decays. The second section contests the claim by Burrage et al. that Chameleon gravity is inconsistent in the early universe, unless constraints on its coupling mechanism are significantly increased. It is shown that the addition of a Dirac-Borne-Infeld (DBI) correction - a consistent, high energy modification - to the Chameleon dynamically renders it weakly coupled to matter. This is done without any fine-tuning and ensures the consistency of the Chameleon at all scales without infringing upon its crucial feature as a dark energy candidate: its elusive but prominent coupling to matter.