Perturbatively constructed cosmological model with periodically distributed dust inhomogeneities

Abstract

We constructed a simple cosmological model which approximates the Einstein-de Sitter background with periodically distributed dust inhomogeneities. By taking the metric as a power series up to the third order in some perturbative parameter $\lambda$, we are able to achieve large values of the density contrast. With a metric explicitly given, many model properties can be calculated in a straightforward way which is interesting in the context of the current discussion concerning the averaging of the inhomogeneities and their backreaction in cosmology. Although the Einstein-de Sitter model can be thought as the model \emph{average}, the light propagation differs from that of the Einstein-de Sitter. The angular diameter distance-redshift relation is affected by the presence of inhomogeneities and depends on the observer's position. The model construction scheme enables some generalizations in the future, so the present work is a step towards more realistic cosmological model described by a relatively simple analytical metric.