Fully Characterizing Axially Symmetric Szekeres Models With Three Data Sets

Abstract

Inhomogeneous exact solutions of General Relativity with zero cosmological constant have been used in the literature to challenge the \Lambda CDM model. From one patch Lema\^itre-Tolman-Bondi (LTB) models to axially symmetric quasi-spherical Szekeres (QSS) Swiss-cheese models, some of them are able to reproduce to a good accuracy the cosmological data. It has been shown in the literature that a zero-\Lambda -LTB model with a central observer can be fully determined by two data sets. We demonstrate that an axially symmetric zero-\Lambda -QSS model with an observer located at the origin can be fully reconstructed from three data sets, number counts, luminosity distance and redshift drift. This is a first step towards a future demonstration involving five data sets and the most general Szekeres model.