Studying the precision of ray tracing techniques with Szekeres models

TL;DR

This paper evaluates the accuracy of standard ray tracing methods in complex cosmological models, comparing approximate schemes with exact solutions in Szekeres models to understand their precision and limitations.

Contribution

It provides a detailed comparison of ray tracing approximations against exact solutions in Szekeres models, highlighting their accuracy and deviations in non-symmetric cases.

Findings

Exact convergence matches gravitational and Doppler contributions in LTB models.

Standard ray tracing approximations deviate significantly in non-symmetric Szekeres models.

Doppler convergence inclusion improves accuracy in some models.

Abstract

The simplest standard ray tracing scheme employing the Born and Limber approximations and neglecting lens-lens coupling is used for computing the convergence along individual rays in mock N-body data based on Szekeres swiss cheese and onion models. The results are compared with the exact convergence computed using the exact Szekeres metric combined with the Sachs formalism. A comparison is also made with an extension of the simple ray tracing scheme which includes the Doppler convergence. The exact convergence is reproduced very precisely as the sum of the gravitational and Doppler convergences along rays in Lemaitre-Tolman-Bondi models. This is not the case when the models are based on non-symmetric Szekeres models. For such models, there is a significant deviation between the exact and ray traced paths and hence also the corresponding convergences.