Investigation of the existence of homogeneous universe models in higher order curvature gravity theories

In this thesis, it is to investigate the existence of homogeneous universe models in space and space-time in higher order gravitational theories called -gravity, depending on the shapes and properties of -gravity functions. In the above expressions, is the Ricci Curvature and is the Gauss-Bonnet term defined with . The above-mentioned theories constitute a generalization of Einstein's General Theory of Relativity in 1916, and form part of attempts to explain the phenomenon of "accelerated expansion of the universe", which is particularly evident from the observation data of 1998. Therefore, it is important to see what kind of changes the construction of cosmological models involve in these new gravity theories compared to relativist cosmological models. We will consider -gravity theory within the framework of Bianchi Type-I and Bianchi Type-III models from the class of spatially homogeneous and anisotropic models, under the assumption that the normal (standard) matter-energy content of the universe is a perfect fluid with a linear barotropic equation of state. In terms of providing mathematical workability, these models will be rotationless and of orthogonal type, that is, the metrics will be diagonal and contain only 3 unknown scale factors. The Bianchi Type-I model is the simplest anisotropic model, and at the same time it does not constitute a generalization of the linear isotropic Robertson-Walker model (flat, open, and closed). Our main goal will be to calculate the field equations in an isometric orthonormal tetrad framework under the effective fluid approach, and to establish the functional form of -gravity with their solutions, scale factors. We will deal with this work in a different way from the very few studies with similar purposes in the literature. Instead of assuming ad hoc preliminary solutions (anzats) in advance, as is done in these; First, the consistency conditions of the field equations with this restriction will be determined under the assumption that the matter-energy content of the universe is a isotropic perfect fluid, and then preliminary solutions will be applied when necessary.