Inhomogeneities in dusty universe - a possible alternative to dark energy?

TL;DR

This paper analytically investigates whether inhomogeneities and extra dimensions can explain the universe's late acceleration, concluding they cannot reverse deceleration if energy conditions hold, challenging some prior claims.

Contribution

It provides an analytical study using the generalized LTB model in higher dimensions, showing inhomogeneities and extra dimensions do not produce acceleration under energy conditions.

Findings

Inhomogeneities and extra dimensions cannot reverse deceleration if energy conditions are obeyed.

Radial acceleration can occur even with positive total deceleration.

Extra dimensions tend to enhance deceleration rather than cause acceleration.

Abstract

There have been of late renewed debates on the role of inhomogeneities to explain the observed late acceleration of the universe. We have looked into the problem analytically with the help of the well known spherically symmetric but inhomogeneous Lemaitre-Tolman-Bondi(LTB) model generalised to higher dimensions. It is observed that in contrast to the claim made by Kolb et al the presence of inhomogeneities as well as extra dimensions can not reverse the signature of the deceleration parameter if the matter field obeys the energy conditions. The well known Raychaudhuri equation also points to the same result. Without solving the field equations explicitly it can, however, be shown that although the total deceleration is positive everywhere nevertheless it does not exclude the possibility of having radial acceleration, even in the pure dust universe, if the angular scale factor is decelerating fast enough and vice versa. Moreover it is found that introduction of extra dimensions can not reverse the scenario. To the contrary it actually helps the decelerating process.