Cosmological backreaction within the Szekeres model and emergence of spatial curvature

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 Ω R (in the FLRW limit Ω R → Ω 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 ΛCDM model, which is spatially flat). In the Styrofoamtype model, which does not have a fixed background, the mean evolution deviates from the spatially flat ΛCDM model, and the mean spatial curvature evolves from Ω R = 0 at the CMB to Ω R ∼ 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. Ω k = 0, even if in the early Universe Ω k = 0) and therefore when analysing low-z cosmological data one should keep Ω k as a free parameter and independent from the CMB constraints.

On average properties of inhomogeneous fluids in general relativity III: general fluid cosmologies

“…Most authors cited in the above discussion base their studies either on a direct 3 + 1 formulation of the evolution and averaged equations, or on a formulation using explicitly 4−covariant terms from which a 3 + 1 form is explicitly deduced. 11 This system of averaged equations is given in a background-independent scheme as a preliminary step in [60,87]. However, the emphasis is subsequently put on linear perturbation theory around a Friedmannian background, on which the main conclusions are based.…”

“…Such effective relations encode inhomogeneous properties and evolution details of the fluid and, hence, they are dynamical and not simply derivable from thermodynamical properties. Closure conditions can be studied in terms of exact scaling solutions [22,28,79], global assumptions on model universes [20,21], exact solutions of the Einstein equations [64,10,83,84,63,85,35,11,86,37] (see also [23, sect.7]), or generic but approximate models for inhomogeneities. The latter may be based on relativistic Lagrangian perturbation theory, e.g.…”

Theoretical cosmology

“…As noted above, attempts to study relativistic models of inhomogeneities rely upon metric forms that are designed to be "close to" the spatially homogeneous and isotropic metric form. However, these can not also be used to address the cosmological backreaction problem; backreaction can only be present if the structure-emerging average spatial curvature, and hence the large-scale average of cosmological variables, are allowed to evolve [141]. A dynamical coupling of matter and geometry on small scales which allows spatial curvature to vary is a natural feature of GR.…”

Constraining dynamical neutrino mass generation with cosmological data

“…due to the local density distribution or late-time emergence of curvature (see e.g. [25] regarding the former and [26] regarding the latter). We therefore choose not to use HST data here.…”