Quasi-Newtonian Cosmological Models in Scalar-Tensor Theories of Gravity

MSc (Physics), North-West University, Mahikeng CampusTheoretical physics in general and cosmology in particular have faced some challenges due to the recent observations in cosmology and astronomy, such as the discovery of the accelerated cosmic expansion and the existence of dark matter and dark energy. Einstein's theory of General Relativity (GR) together with the standard model of cosmology fall short of giving any explanations for these problems. Higher-order gravitational theories such as f (R) and scalar-tensor theories of gravity have been suggested to provide an answer to these shortcomings. In this dissertation, we investigate the cosmological implications of such theories such as the background expansion history as well as the evolution of cosmological density perturbations. We present the equivalence between f (R) and scalar-tensor theories of gravity and we exploit this equivalence to discuss some simple procedures to reconstruct f (R) gravity models from the Chaplygin scalar field in flat de Sitter spacetimes. We derive the Lagrangian densities for the f (R) action and we get the exact f (R) models and the corresponding scalar field potentials for asymptotically de Sitter spacetimes in early and late epochs. We also reconstruct f (R) from the exact cosmological solutions of the Einstein field equations with a non-interacting classical scalar field-and-radiation with predetermined inflationary expansion scenarios of the Friedmann-Lemaitre-Robertson-Walker (FLRW) background spacetime, and we get the corresponding potentials for the scalar field. We calculate the slow-roll parameters (the spectral index n 8 and the tensor-to-scalar ratio r) to show how these parameters can be constrained by observational data. Although GR is a generalization of Newtonian gravity in the presence of strong gravitational fields, there is no properly defined Newtonian limit of GR on cosmological scales. Recently, general relativistic quasi-Newtonian cosmologies have been studied in the context of large-scale structure formation and nonlinear gravitational collapse in the late-time universe. This despite the general covariant inconsistency of these cosmological models except in some special cases such as the spatially homogeneous and isotropic, spherically symmetric, expanding FLRW spacetimes. f (R) models have been shown to exhibit more shared properties with Newtonian gravitation than does GR. We investigate the existence and integrability conditions of quasi-Newtonian cosmological spacetimes of classes of shear-free cosmological dust models with irrotational fluid flows in the context of scalar-tensor theories of gravity. We also derive the covariant density and velocity propagation equations of such models and analyse the corresponding solutions to these perturbation equations.Master