Fully Characterizing Axially Symmetric Szekeres Models With Three Data Sets

TL;DR

This paper demonstrates that an axially symmetric Szekeres cosmological model can be fully reconstructed using three specific data sets, advancing the understanding of inhomogeneous solutions in General Relativity.

Contribution

It shows that three data sets are sufficient to fully determine an axially symmetric Szekeres model, extending previous results from simpler models.

Findings

Model can be reconstructed from three data sets.

Reconstruction includes number counts, luminosity distance, and redshift drift.

First step towards general Szekeres model reconstruction.

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.