Having as a starting point the problem of dark energy described before, this thesis studies modifications of General Relativity (GR), as possible gravitational scenarios for the early and late time Universe, motivated by both classical as well as quantum considerations. In particular, it focuses on modifications of GR of the type f(R) as well as the f(R;G) ones, where R and G is the Ricci scalar and Gauss-Bonnet term respectively. On the same time, a modification of GR based on the Renormalisation Group approach to quantum gravity is considered, as well as its link to f(R) gravity. The main goal of the investigations carried out in this thesis, is to understand the structure, as well as the phenomenological implications of non-linear modifications of GR for cosmology, at both the background as well as the linear perturbation level. In particular, chapter 2 presents a brief introduction to the dynamics of GR in the presence of a "dark component" at the background, as well as at the linear perturbation level, while chapter 3 is an introduction to the fundamental properties of non-linear modifications of GR, reviewing important results of the relevant literature. Chapter 4 elaborates with a fundamental property of non{linear gravity models, namely the study of different representations of vacuum actions proportional to f(R) as well as f(G), in view of Legendre transformations, for the case of spacetime manifolds with a boundary. As it is explicitly shown there, although the dynamical equivalence is always true in the bulk, it is not guaranteed on the boundary of the spacetime manifold. On the other hand, chapter 5 focuses on understanding the role of the effective anisotropic stress present in f(R;G) gravity models, attempting to construct particular models of the latter type, with a vanishingly small anisotropic stress, so as to agree with current observations. As it turns out, suppression of the effective anisotropic stress in this class of models is very difficult, highlighting the role of the effective anisotropic stress as a smoking gun for testing modified gravity models with current and future observations. Chapter 6 serves as an introduction to the idea of the Renormalisation Group (RG) and its applications in cosmology, while chapter 7 starts from an RG improved Einstein{Hilbert action and studies its connection with f(R) gravity, as well as its implications for the primordial and the late time acceleration of the Universe. It is shown that the effective f(R) model has some remarkable properties and interesting implications for both early and late time cosmology.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:589099 |
| Date | January 2013 |
| Creators | Saltas, Ippocratis D. |
| Publisher | University of Sussex |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
| Source | http://sro.sussex.ac.uk/id/eprint/47329/ |
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