The Study of Inhomogeneous Cosmologies Through Spacetime Matchings

Our universe is inherently inhomogeneous yet it is common in the study of cosmology to model our universe after the homogeneous and isotropic Friedmann-Lemaıtre-Roberson-Walker (FLRW) model. In this thesis spacetime matchings are applied to investigate more general inhomogeneous cosmologies. The Cheese Slice universe, constructed from matching together FLRW and Kasner regions satisfying the Darmois matching conditions, is used as a prime example of an inhomogeneous cosmology. Some observational consequences of this model are presented. The lookback time verses redshift relation is calculated using a numerical algorithm and it is shown that the relative thickness of the Kasner regions have the greatest impact on anisotropies an observer would see. The number of layers and distribution of layers play a smaller role in this regard. The relative thickness of the Kasner slice should be on the order of one ten thousandth the thickness of the FLRW regions to have the anisotropies fall within the observed CMB limit. The approach to the singularity of a spacetime matching is examined. A criterion is presented for a matched spacetime to be considered Asymptotically Velocity Term Dominated (AVTD). Both sides of the matching must be AVTD and each leaf of the respective foliations mush match as well. It is demonstrated that the open and flat Cheese Slice universe are both AVTD and the singularity is also of AVTD type. The Cheese Slice model is then examined as a braneworld construction. The possibility of a Cheese Slice brane satisfying all the energy conditions is shown. However, the embedding of such a brane into a symmetric bulk is non-trivial. The general embedding of a matched spacetime into a bulk is investigated using a Taylor series approximation of the bulk. It is found that the energy-momentum tensor of such a brane cannot have discrete jumps if the embedding does not have a corner. A 3+1+1 decomposition of the bulk spacetime is then carried out. With the spacetime being deconstructed along two preferred timelike hypersurfaces, this becomes a natural environment to discuss the matching of branes. We find that there are conditions on the matter content of the branes to be matched if an observer on the brane is to see the matching surface as a boundary surface with no additional stress energy. Matching more than two bulks is also examined and shown to allow for more general brane configurations.Ph