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

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. Our aim is to show that L--T models exist that reproduce a few features of the $Λ$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 $Λ$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.