Cosmography with $\Lambda$-Szekeres Models

TL;DR

This paper develops a fourth-order cosmography framework for luminosity distance and tests it within axially symmetric Szekeres models to evaluate its accuracy in inhomogeneous cosmological structures.

Contribution

It derives a fourth-order luminosity distance cosmography and applies it to Szekeres models to assess its effectiveness in inhomogeneous universes.

Findings

Cosmography accurately approximates distance-redshift relations in Szekeres models.

The approximation level varies with the inhomogeneity and observer position.

Results support covariant cosmography as a useful model-independent analysis tool.

Abstract

The cosmological tensions present in the $\Lambda$ cold dark matter model that have emerged and strengthened over recent years motivate model independent approaches to analysing data. Cosmography is useful for interpreting data in cosmology without imposing assumptions about the field equations of gravity or the matter content in the Universe. Some cosmography methods, denoted covariant cosmography, go even further and stay agnostic to the underlying space-time metric. Due to their high level of generality, covariant cosmography methods can incorporate the anisotropies and inhomogeneities in the observer's vicinity, and may in turn inform about the associated curvature of the relevant structures in our cosmic neighbourhood. Thus, covariant cosmography is a powerful model-independent tool for analysing cosmological data while also enabling the mapping of our local cosmic neighbourhood. In order to be able to explore the covariant cosmography framework to its fullest, it must be tested in tractable models and simulations. In this paper we derive the cosmography of luminosity distance to fourth order in redshift and investigate it in the special case of axially symmetric Szekeres models. We compare the numerical results for the distance-redshift relations of synthetic observers placed within the Szekeres structures with the predictions from the cosmography, and comment on the found level of approximation of the cosmography in relation to other results in the litterature.