Modelling Inhomogeneity in the Universe
An overview of some recent developments in inhomogeneous models is presented. As the volume and precision of cosmological data improves, it will become more and more essential to understand the non-linear behaviour of the Einstein field equations. This requires the study of exact inhomogeneous solutions, including their density distributions, their evolution, their geometry, and their causal structure. Observations are strongly affected by the detailed geometry and evolution of a model, and therefore interpretation of observations depends on understanding them. It is generally assumed the universe is homogeneous if averaged over large enough scales, but to actually prove this is so, will require the assumption to be relaxed, and a rigorous inhomogeneous approach to be applied. Though the Lemaitre-Tolman metric has long been used for models of spherical inhomogeneities, there have been a number of new results, including a variety of methods for creating models with specific properties, and their application to cosmic structures on several different scales. Interest in the Szekeres metrics is on the increase, and the quasi-spherical metric was recently used to model specific cosmic structures for the first time. The quasi-planar and quasi-hyperspherical metrics have been hardly studied until recent work invesigated their physical and geometric properties. There is enormous scope for work with these metrics.