Average luminosity distance in inhomogeneous universes

TL;DR

This study uses exact, non-perturbative numerical ray tracing in inhomogeneous universe models to quantify how local structures affect the average luminosity distance measurements, providing insights relevant for cosmological observations.

Contribution

It introduces a novel, exact averaging method including supernovae within voids, and derives a formula for maximum average correction as a function of redshift.

Findings

Average distance modulus correction at low redshift is non-zero due to peculiar velocities.

The maximum correction formula agrees well with numerical results.

Actual corrections are damped below the maximum due to cancelations between void effects.

Abstract

Using numerical ray tracing, the paper studies how the average distance modulus in an inhomogeneous universe differs from its homogeneous counterpart. The averaging is over all directions from a fixed observer not over all possible observers (cosmic), thus it is more directly applicable to our observations. Unlike previous studies, the averaging is exact, non-perturbative, and includes all possible non-linear effects. The inhomogeneous universes are represented by Sweese-cheese models containing random and simple cubic lattices of mass-compensated voids. The Earth observer is in the homogeneous cheese which has an Einstein - de Sitter metric. For the first time, the averaging is widened to include the supernovas inside the voids by assuming the probability for supernova emission from any comoving volume is proportional to the rest mass in it. Despite the well known argument for photon flux conservation, the average distance modulus correction at low redshifts is not zero due to the peculiar velocities. A formula for the maximum possible average correction as a function of redshift is derived and shown to be in excellent agreement with the numerical results. The actual average correction calculated in random and simple cubic void lattices is severely damped below the predicted maximal average. That is traced to cancelations between the corrections coming from the fronts and backs of different voids at the same redshift from the observer. The calculated correction at low redshifts allows one to readily predict the redshift at which the averaged fluctuation in the Hubble diagram is below a required precision and suggests a method to extract the background Hubble constant from low redshift data without the need to correct for peculiar velocities.