A new type of exact arbitrarily inhomogeneous cosmology: evolution of deceleration in the flat homogeneous-on-average case

Abstract

A new method for constructing exact inhomogeneous universes is presented, that allows variation in 3 dimensions. The resulting spacetime may be statistically uniform on average, or have random, non-repeating variation. The construction utilises the Darmois junction conditions to join many different component spacetime regions. In the initial simple example given, the component parts are spatially flat and uniform, but much more general combinations should be possible. Further inhomogeneity may be added via swiss cheese vacuoles and inhomogeneous metrics. This model is used to explore the proposal, that observers are located in bound, non-expanding regions, while the universe is actually in the process of becoming void dominated, and thus its average expansion rate is increasing. The model confirms qualitatively that the faster expanding components come to dominate the average, and that inhomogeneity results in average parameters which evolve differently from those of any one component, but more realistic modelling of the effect will need this construction to be generalised.