Ray tracing and Hubble diagrams in post-Newtonian cosmology

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-Lemaître-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.

37 pages, 15 figures, 1 table, v2: matches published version

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