Standard models of cosmology use inflation as a mechanism to resolve the isotropy and homogeneity problem of the universe as well as the flatness problem. However, due to various well known problems with the inflationary paradigm, there has been an ongoing search for alternatives. Perhaps the most famous among these are the cyclic universe scenarios which incorporate bounces. As these scenarios have a contracting phase in the evolution of the universe, anisotropies and inhomogeneities would be expected to blow up on approach to the bounce. Thus, it is reasonable to ask whether the problems of homogeneity and isotropy can still be resolved in these scenarios. In this thesis, I will focus on the problem of the resolution of the isotropy problem. I begin with a brief review of anisotropic, spatially homogeneous geometries of cosmological interest. Next, I review the existing literature on bouncing cosmologies, and discuss the mechanism of bounce studied in previously proposed models, as well as their theoretical and observational advantages and disadvantages. I then discuss the process of isotropisation in the contracting phase of each bounce. In this phase of the evolution, the mechanism of ekpyrosis is used in most cosmological scenarios which incorporate a contracting phase to mitigate the problem of anisotropies blowing up on approaching the bounce. I start by studying anisotropic universes and I then examine the effect of the addition of ultra-stiff anisotropic pressures on the ekpyrotic phase. I then consider evolving such anisotropic universes through several cycles with increasing expansion maxima at each successive bounce. This eventually leads to flatness in the isotropic case. My aim is to see if the resolution of the flatness problem also leads to a simultaneous resolution of the isotropy problem. In the next chapter, I consider the effect of non comoving velocities on the shape of this anisotropic bouncing universe. In the final section of my thesis, I consider anisotropic cosmological models within the context of canonical quantum cosmology and investigate the quantum behaviour of anisotropies.

abstract: Two ideas that extends on the theory of General Relativity are introduced and then the phenomenology they can offer is explored. The first idea shows how certain types of $f(R)$ gravity allows for traversable wormholes among its vacuum solutions. This is surprising to find in such simple setting as these type of solutions usually requires fairly complex constructions to satisfy the equations of motion of a gravitational theory. The second idea is the matter bounce description of the early universe where a fairly unique feature of the model is identified. Consequences of this feature could allow the paradigm to distinguish itself from other alternative descriptions, such as inflation, through late time observations. An explicit example of this claim is worked out by studying a model involving an interaction in the dark sector. Results of a more astrophysical nature, where a careful analysis of the morphology of blazar halos is performed, are also presented in the Appendix. The analysis determined that the $Q$-statistic is an appropriate tool to probe the properties of the intergalactic magnetic fields responsible for the halos formation. / Dissertation/Thesis / Doctoral Dissertation Physics 2017