On the Observational Characteristics of Inhomogeneous Cosmologies: Undermining the Cosmological Principle or Have Cosmologists Put All Their EGs in One Basket

This thesis concerns the compatibility of inhomogeneous cosmologies with our present understanding of the universe. It is a problem of some interest to find the class of all relativistic cosmological models which are capable of providing a reasonable 'fit' to the universe. One can imagine building up an (infinite-dimensional) parameter space containing all cosmological models. At any time the understanding of the universe would represent a blob in parameter space in which, presumably, the real universe would sit. This thesis, in some respects, is part of this process. We consider Stephani models, which are a generalisation of the standard Friedmann-Lemaitre-Robertson-Walker (FLRW) models, which can be thought of as FLRW models with curvature which changes over time. This changing curvature reflects the existence of spatial pressure gradients which leads to an acceleration of the fundamental observers. Thus these models generalise the 'dust' assumption of standard cosmology. Models normally considered in the 'classification scheme' approach are usually homogeneous dust or barotropic perfect fluid models. They are anisotropic however, and thus generalise the FLRW models. Most importantly, because these models are homogeneous, they satisfy the Copernican principle. The crucial aspect of this work is the retention of the Copernican principle - an assumption regarded by many as crucial to cosmology. It states that we are not at a special location in the universe. This is a vital aspect of the original work in this thesis: consideration of an inhomogeneous model, while retaining the Copernican principle has, as far as the author is aware, not been considered in detail before. One may formulate the Copernican principle in many ways, from assuming we are not at a special location, to assuming that all (or most) locations are equivalent, which more or less forces homogeneity. Because the models considered here are inhomogeneous, they cannot satisfy the stronger version of the Copernican principle entirely - all locations will not be equivalent. However, we may demand that they are observationally indistinguishable. This is the tactic we use here. En route to this goal we must therefore calculate all observable quantities at any location in the spacetime. Certain properties of the Stephani models we consider allow us to do this exactly: consequently, many results of this thesis present, for the first time, observational relations for a class of inhomogeneous cosmological models which are exact, and valid for any observer position in the spacetime. It may reasonably be claimed that the standard model is perfectly acceptable. However, a number of the properties of the models considered here do make them rather appealing. For example it is shown i