Averaging procedure in variable-G cosmologies

TL;DR

This paper extends averaging formalisms in cosmology to include variable Newton's constant and cosmological term, linking quantum gravity renormalization ideas with inhomogeneity effects and dark energy phenomenology.

Contribution

It introduces a formalism for averaged cosmological equations with variable G and Lambda, incorporating quantum gravity insights and inhomogeneity effects.

Findings

Survival of backreaction and curvature coupling in variable-G models

Emergence of a variable-G cosmic quintet

Approximate early universe FLRW solution with inhomogeneities accounted for

Abstract

Previous work in the literature had built a formalism for spatially averaged equations for the scale factor, giving rise to an averaged Raychaudhuri equation and averaged Hamiltonian constraint, which involve a backreaction source term. The present paper extends these equations to include models with variable Newton parameter and variable cosmological term, motivated by the nonperturbative renormalization program for quantum gravity based upon the Einstein-Hilbert action. We focus on the Brans-Dicke form of the renormalization-group improved action functional. The coupling between backreaction and spatially averaged three-dimensional scalar curvature is found to survive, and a variable-G cosmic quintet is found to emerge. Interestingly, under suitable assumptions, an approximate solution can be found where the early universe tends to a FLRW model, while keeping track of the original inhomogeneities through three effective fluids. The resulting qualitative picture is that of a universe consisting of baryons only, while inhomogeneities average out to give rise to the full dark-side phenomenology.