The $m$-$z$ relation for Type Ia supernovae: safety in numbers or safely without worry?

TL;DR

This paper examines whether the observed $m$-$z$ relation for Type Ia supernovae reliably supports the cosmological concordance model, concluding that the assumption of homogeneity along lines of sight is justified, allowing safe use of traditional luminosity distance formulas.

Contribution

It demonstrates that the $m$-$z$ relation is consistent with a homogeneous universe, validating the use of standard formulas in cosmological analyses.

Findings

Statistical analysis favors homogeneity along lines of sight.

The traditional luminosity distance formula is justified.

No significant correlation found between residuals and observational uncertainties.

Abstract

The $m$-$z$ relation for Type Ia supernovae is compatible with the cosmological concordance model if one assumes that the Universe is homogeneous, at least with respect to light propagation. This could be due to the density along each line of sight being equal to the overall cosmological density, or to `safety in numbers', with variation in the density along all lines of sight averaging out if the sample is large enough. Statistical correlations (or lack thereof) between redshifts, residuals (differences between the observed distance moduli and those calculated from the best-fitting cosmological model), and observational uncertainties suggest that the former scenario is the better description, so that one can use the traditional formula for the luminosity distance safely without worry.