Cosmological backreaction within the Szekeres model and emergence of
  spatial curvature
  This paper discusses the phenomenon of backreaction within the Szekeres
model. Cosmological backreaction describes how the mean global evolution of the
Universe deviates from the Friedmannian evolution. The analysis is based on
models of a single cosmological environment and the global ensemble of the
Szekeres models (of the Swiss-Cheese-type and Styrofoam-type). The obtained
results show that non-linear growth of cosmic structures is associated with the
growth of the spatial curvature $\Omega_{\cal R}$ (in the FLRW limit
$\Omega_{\cal R} \to \Omega_k$). If averaged over global scales the result
depends on the assumed global model of the Universe. Within the Swiss-Cheese
model, which does have a fixed background, the volume average follows the
evolution of the background, and the global spatial curvature averages out to
zero (the background model is the $\Lambda$CDM model, which is spatially flat).
In the Styrofoam-type model, which does not have a fixed background, the mean
evolution deviates from the spatially flat $\Lambda$CDM model, and the mean
spatial curvature evolves to from $\Omega_{\cal R} =0 $ at the CMB to
$\Omega_{\cal R} \sim 0.1$ at $z =0$. If the Styrofoam-type model correctly
captures evolutionary features of the real Universe then one should expect that
in our Universe, the spatial curvature should build up (local growth of cosmic
structures) and its mean global average should deviate from zero
(backreaction). As a result, this paper predicts that the low-redshift Universe
should not be spatially flat (i.e. $\Omega_k \ne 0$, even if in the early
Universe $\Omega_k = 0$) and therefore when analysing low-$z$ cosmological data
one should keep $\Omega_k$ as a free parameter and independent from the CMB
constraints.
