# Cosmological backreaction within the Szekeres model and emergence of spatial curvature

## TL;DR

This paper investigates how non-linear cosmic structure growth within the Szekeres model influences spatial curvature, suggesting that the Universe's low-redshift spatial curvature may deviate from zero due to backreaction effects.

## Contribution

It demonstrates that the evolution of spatial curvature depends on the global model, showing that backreaction can lead to a non-zero curvature at low redshifts in the Styrofoam-type Szekeres model.

## Key findings

- In Swiss-Cheese models, the average curvature remains zero, following the background.
- In Styrofoam-type models, the average curvature grows to about 0.1 at present.
- The results imply low-redshift Universe may have non-zero spatial curvature due to backreaction.

## Abstract

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.