Luminosity distance and redshift in the Szekeres inhomogeneous cosmological models

TL;DR

This paper develops a numerical framework to compute luminosity distance and redshift in the general Szekeres inhomogeneous cosmological models, enabling more accurate modeling of the universe's true lumpy structure.

Contribution

It introduces a method to integrate distances and redshift in the most general Szekeres models without symmetry assumptions, expanding their applicability.

Findings

Framework for numerical integration of distances in Szekeres models

Derivation of differential equations for null geodesics and redshift

Potential for improved comparison with cosmological observations

Abstract

The Szekeres inhomogeneous models can be used to model the true lumpy universe that we observe. This family of exact solutions to Einstein's equations was originally derived with a general metric that has no symmetries. In this work, we develop and use a framework to integrate the angular diameter and luminosity distances in the general Szekeres models. We use the affine null geodesic equations in order to derive a set of first-order ordinary differential equations that can be integrated numerically to calculate the partial derivatives of the null vector components. These equations allow the integration in all generality of the distances in the Szekeres models and some examples are given. The redshift is determined from simultaneous integration of the null geodesic equations. This work does not assume spherical or axial symmetry, and the results will be useful for comparisons of the general Szekeres inhomogeneous models to current and future cosmological data.