Averaging procedure in variable - G cosmologies

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 non perturbative renormalization program for quantum gravity based upon the Einstein–Hilbert action. The coupling between backreaction and spatially averaged three-dimensional scalar curvature is found to survive, and all equations involving contributions of a variable Newton parameter are worked out in detail. Interestingly, under suitable assumptions, an approximate solution can be found where the universe tends to a FLRW model, while keeping track of the original inhomogeneities through two effective fluids. PACS numbers: 04.50.+h, 98.80.-k, 98.80.Es