TL;DR
This paper investigates how local inhomogeneities influence the overall expansion of the universe within a perturbative framework, providing a gauge-invariant expression for back-reaction effects and quantifying their impact.
Contribution
It introduces a generic linearized averaging method for metric perturbations and derives a gauge-invariant formula for back-reaction in perturbed FLRW universes, including velocity and vorticity effects.
Findings
Derived a gauge-invariant back-reaction expression in terms of observable quantities
Quantitatively assessed the impact of density inhomogeneities on cosmic expansion
Compared results with existing literature to validate approach
Abstract
In this paper we discuss the effect of local inhomogeneities on the global expansion of nearly FLRW universes, in a perturbative setting. We derive a generic linearized averaging operation for metric perturbations from basic assumptions, and we explicify the issue of gauge invariance. We derive a gauge invariant expression for the back-reaction of density inhomogeneities on the global expansion of perturbed FLRW spacetimes, in terms of observable quantities, and we calculate the effect quantitatively. Since we do not adopt a comoving gauge, our result incorporates the back-reaction on the metric due to scalar velocity and vorticity perturbations. The results are compared with the results by other authors in this field.
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