Redshift drift in axially symmetric quasi-spherical Szekeres models

TL;DR

This paper calculates the redshift drift in a specific inhomogeneous cosmological model, demonstrating its effectiveness in distinguishing between different universe models like DM and LTB, and discusses how to fully constrain the model's parameters.

Contribution

It provides the first computation of redshift drift for an axially symmetric quasi-spherical Szekeres Swiss-cheese model and compares it with other cosmological models to assess its discriminative power.

Findings

Redshift drift differs significantly between models, serving as an effective discriminator.

The Szekeres model can reproduce supernova data accurately.

A method to fully constrain the model's degrees of freedom is proposed.

Abstract

Models of inhomogeneous universes constructed with exact solutions of Einstein's General Relativity have been proposed in the literature with the aim of reproducing the cosmological data without any need for a dark energy component. Besides large scale inhomogeneity models spherically symmetric around the observer, Swiss-cheese models have also been studied. Among them, Swiss-cheeses where the inhomogeneous patches are modeled by different particular Szekeres solutions have been used for reproducing the apparent dimming of the type Ia supernovae (SNIa). However, the problem of fitting such models to the SNIa data is completely degenerate and we need other constraints to fully characterize them. One of the tests which is known to be able to discriminate between different cosmological models is the redshift-drift. This drift has already been calculated by different authors for Lema\^itre-Tolman-Bondi (LTB) models. We compute it here for one particular axially symmetric quasi-spherical Szekeres (QSS) Swiss-cheese which has previously been shown to reproduce to a good accuracy the SNIa data, and we compare the results to the drift in the $\Lambda$CDM model and in some LTB models that can be found in the literature. We show that it is a good discriminator between them. Then, we discuss our model's remaining degrees of freedom and propose a recipe to fully constrain them.