Calculating Observables in Inhomogeneous Cosmologies I: General Framework

TL;DR

This paper develops a general numerical framework for computing cosmological observables in inhomogeneous universes, including those with no spherical symmetry, and applies it to the Szekeres metric.

Contribution

It introduces a versatile algorithm based on null geodesic equations for calculating observables in arbitrary inhomogeneous cosmologies, extending beyond symmetric models.

Findings

Algorithm successfully tracks light rays in inhomogeneous spacetimes.

Framework accommodates observables like proper motions and redshift-space density.

Application to Szekeres metric demonstrates practical implementation.

Abstract

We lay out a general framework for calculating the variation of a set of cosmological observables, down the past null cone of an arbitrarily placed observer, in a given arbitrary inhomogeneous metric. The observables include redshift, proper motions, area distance and redshift-space density. Of particular interest are observables that are zero in the spherically symmetric case, such as proper motions. The algorithm is based on the null geodesic equation and the geodesic deviation equation, and it is tailored to creating a practical numerical implementation. The algorithm provides a method for tracking which light rays connect moving objects to the observer at successive times. Our algorithm is applied to the particular case of the Szekeres metric. A numerical implementation has been created and some results will be presented in a subsequent paper. Future work will explore the range of possibilities.