Inhomogeneous dusty Universes and their deceleration

Abstract

Exact results stemming directly from Einstein equations imply that inhomogeneous Universes endowed with vanishing pressure density can only decelerate, unless the energy density of the Universe becomes negative. Recent proposals seem to argue that inhomogeneous (but isotropic) space-times, filled only with incoherent matter,may turn into accelerated Universes for sufficiently late times. To scrutinize these scenarios, fully inhomogeneous Einstein equations are discussed in the synchronous system. In a dust-dominated Universe, the inhomogeneous generalization of the deceleration parameter is always positive semi-definite implying that no acceleration takes place.