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 λ, 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 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.

Construction of the cosmological model with periodically distributed inhomogeneities with growing amplitude

“…It is rather a step toward understanding the role of the large-scale inhomogeneities in the interpretation of the cosmological observables. The present paper is a large improvement of our previous work [77,78], but many issues could be done better in the future. First of all, there is a much more challenging task of considering perturbations around the nonflat background with nonzero cosmological constant.…”

“…The scalar perturbations in the linear order admit two modes: the decaying and the growing one. In our previous paper [78], we analyze the decaying mode consistent with the assumption (i) in the orders higher than the linear order. In the current paper, we concentrate on the growing mode.…”

“…Then, we consider the resulting fourth-order metric as the polynomial in the perturbative parameter and calculate the exact Einstein tensor. This way, we analyze the higher-order contributions, what is the main improvement compared to our previous papers [77,78]. We interpret the pressure-like terms of the energymomentum tensor in the framework of the Jeans' theory of the collisionless system of particles.…”

“…The principal goal of this paper is to find a cosmological model which remains dust-like within the observational constraints, but at the same time allows much higher amplitude of the inhomogeneities than the linear perturbation theory. We studied decaying mode of the linear perturbation theory in [77] and expanded it to the third-order perturbations in [78]. In the recent paper, we consider the growing mode of the perturbation theory up to the fourth order.…”

“…3.2 that for a large amplitude of the inhomogeneities considered, the third-order perturbations do not satisfy the observational constraints of the pressure value in the matter-dominated era, while the fourth-order model does. This way, we investigate the convergence of our perturbative framework, which is an improvement compared to our previous papers [77,78].…”