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

Abstract

Context. Lemaître-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. Aims. Our aim is to show that L-T models exist that reproduce a few features of the ΛCDM model, but do not contain the giant cosmic void. Methods. 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 ΛCDM 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. Results. 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.

Cosmological fractal matter with an upper cutoff

“…10. However one caveat to these inhomogeneous LTB models is that under very mild assumptions on regularity and asymptotic behavior of the free functions of the LTB model, any pair of sets of conjugate observational data (for instance the pairs {angular diameter distance, mass density in the redshift space} or {angular diameter distance, expansion rate}) can be reproduced 11,12 . Proposing an alternative to the FLRW model which has so much freedom that it can fit any data sets seems problematic.…”

Averaged Lemaître–Tolman–Bondi dynamics

“…There exists a large body of literature on cosmological models relying on the LTB dynamics, see, e.g., [22][23][24][25][26][27][28][29][30]. Our interest here is not primarily whether or not these inhomogeneous models can provide viable alternatives to the standard ΛCDM model.…”

Editorial note to: H. P. Robertson, Relativistic cosmology

“…9 But this is not a good model universe as it has no redshifts and is unstable. He then presents the expanding de Sitter solution in the stationary (k = 0) frame (6.1), showing it must be an empty spacetime if we apply the energy conditions ρ ≥ 0, p ≥ 0.…”