A (giant) void is not mandatory to explain away dark energy with a Lemaitre - Tolman model

TL;DR

This paper demonstrates that Lemaître-Tolman models can explain supernova observations without requiring a giant cosmic void, challenging previous claims that such voids are necessary to account for dark energy effects.

Contribution

The authors show that non-void L-T models can replicate key features of the ΛCDM model, using general initial data, thus removing the need for a giant void in explaining cosmic acceleration.

Findings

L-T models without a giant void can match ΛCDM features

A giant hump in density profile replaces the void in these models

The existence of a giant void is due to limited assumptions in earlier models

Abstract

Lema\^itre - Tolman (L--T) toy models with a central observer have been used to study the effect of large scale inhomogeneities on the SN Ia dimming. Claims that a giant void is mandatory to explain away dark energy in this framework are currently dominating. Our aim is to show that L-T models exist that reproduce a few features of the $\Lambda$CDM model, but do not contain the giant cosmic void. We propose to use two sets of data - the angular diameter distance together with the redshift-space mass-density and the angular diameter distance together with the expansion rate - both defined on the past null cone as functions of the redshift. We assume that these functions are of the same form as in the $\Lambda$CDM model. Using the Mustapha-Hellaby-Ellis algorithm, we numerically transform these initial data into the usual two L-T arbitrary functions and solve the evolution equation to calculate the mass distribution in spacetime. For both models, we find that the current density profile does not exhibit a giant void, but rather a giant hump. However, this hump is not directly observable, since it is in a spacelike relation to a present observer. The alleged existence of the giant void was a consequence of the L-T models used earlier because their generality was limited a priori by needless simplifying assumptions, like, for example, the bang-time function being constant. Instead, one can feed any mass distribution or expansion rate history on the past light cone as initial data to the L-T evolution equation. When a fully general L-T metric is used, the giant void is not implied.