# Ray tracing and Hubble diagrams in post-Newtonian cosmology

## TL;DR

This paper investigates how small-scale inhomogeneities and opaque objects in the universe affect light propagation and cosmological measurements, revealing potential biases in estimating dark energy parameters.

## Contribution

It introduces a method to compute redshifts and luminosity distances in inhomogeneous cosmologies with large density contrasts, highlighting the impact of opaque objects on observational biases.

## Key findings

- Opaque objects cause a 10% shift in distance measures.
- Photon trajectories avoid high-curvature regions due to opaque objects.
- Selection effects can bias estimates of cosmological parameters.

## Abstract

On small scales the observable Universe is highly inhomogeneous, with galaxies and clusters forming a complex web of voids and filaments. The optical properties of such configurations can be quite different from the perfectly smooth Friedmann-Lema\^itre-Robertson-Walker (FLRW) solutions that are frequently used in cosmology, and must be well understood if we are to make precise inferences about fundamental physics from cosmological observations. We investigate this problem by calculating redshifts and luminosity distances within a class of cosmological models that are constructed explicitly in order to allow for large density contrasts on small scales. Our study of optics is then achieved by propagating one hundred thousand null geodesics through such space-times, with matter arranged in either compact opaque objects or diffuse transparent haloes. We find that in the absence of opaque objects, the mean of our ray tracing results faithfully reproduces the expectations from FLRW cosmology. When opaque objects with sizes similar to those of galactic bulges are introduced, however, we find that the mean of distance measures can be shifted up from FLRW predictions by as much as $10\%$. This bias is due to the viable photon trajectories being restricted by the presence of the opaque objects, which means that they cannot probe the regions of space-time with the highest curvature. It corresponds to a positive bias of order $10\%$ in the estimation of $\Omega_{\Lambda}$ and highlights the important consequences that astronomical selection effects can have on cosmological observables.