Inhomogeneous dusty Universes and their deceleration

TL;DR

This paper demonstrates through Einstein equations that inhomogeneous dust-filled universes cannot accelerate unless they have negative energy density, challenging recent claims of late-time acceleration in such models.

Contribution

It provides a rigorous analysis of inhomogeneous Einstein equations showing that dust universes cannot accelerate without negative energy density, clarifying misconceptions.

Findings

Inhomogeneous dust universes always decelerate.

Acceleration requires negative energy density.

Inhomogeneous models do not produce late-time acceleration.

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.