Mimicking the cosmological constant for more than one observable with large scale inhomogeneities

Abstract

Assuming the definition of the inversion problem (IP) as the exact matching of the terms in the low redshift expansion of cosmological observables calculated for different cosmological models, we solve the IP for D L (z) and the redshift spherical shell mass density mn(z) for a central observer in a LTB space without cosmological constant and a generic ΛCDM model. We show that the solution of the IP is unique, corresponds to a matter density profile which is not smooth at the center and that the same conclusions can be reached expanding self-consistently to any order all the relevant quantities.On contrary to the case of a single observable inversion problem, it is impossible to solve the IP (LTB vs. ΛCDM) for both mn(z) and D L (z) while setting one the two functions k(r) or t b (r) to zero, even allowing not smooth matter profiles. Our conclusions are general, since they are exclusively based on comparing directly physical observables in redshift space, and don't depend on any special ansatz or restriction for the functions defining a LTB model.

Inhomogeneous cosmological models: exact solutions and their applications

“…density profile at the origin with vanishing first derivative, then one obtains that the luminosity distance within the LT model and the FLRW model are the same up to the second order [163], which implies that the deceleration parameter for pure dust models must be positive. This, however, does not have any serious cosmological implications as, first, density does not need to be smooth [144], and, secondly, models with a smooth density profile can also fit the data without dark energy (for example most of the giant void models have a smooth density distribution, see section 4.1).…”

Observational constraints on inhomogeneous cosmological models without dark energy

“…It is enough to adjust one free function (e.g. the curvature) to obtain any distance-redshift relation 11 , as stated by [75] and illustrated, for example, by [83,87] where the luminosity distance of the concordance model is reproduced (see also [96]). By adjusting the other free function, it is also possible to obtain the light-cone matter density (or galaxy number count) of the concordance model [87].…”

Testing the void against cosmological data: fitting CMB, BAO, SN andH0

“…While it is well established that a local Void can mimic an accelerated expansion [3,4,5,6,7,8,9,10,13,14,24], whether such a Void can successfully reproduce all current cosmological data is still a matter of debate. Most work on the void models have focused on reproducing the shape of the ΛCDM luminosity distance (D L ) versus redshift (z) curve, in order to fit the type Ia Supernova data, but a few studies [14,15,16] have included other data such as Cosmic Microwave Background (CMB) and Baryon Acoustic Oscillations scale (BAO).…”