Emergence of smooth distance and apparent magnitude in a lumpy Universe

TL;DR

This paper investigates how inhomogeneities in the universe affect the observed apparent magnitude of Type Ia supernovae, revealing potential corrections and implications for cosmological measurements like the Hubble rate.

Contribution

It introduces a method to account for inhomogeneities in the universe when analyzing supernova data, highlighting their impact on apparent magnitude and Hubble residuals.

Findings

Velocity perturbations affect low-redshift apparent magnitudes.

Inhomogeneities contribute to Hubble residual variance.

Corrections may resolve Hubble rate measurement tensions.

Abstract

The standard interpretation of observations such as the peak apparent magnitude of Type Ia supernova made from one location in a lumpy Universe is based on the idealised Friedmann-Lema\^itre Robertson-Walker spacetime. All possible corrections to this model due to inhomogeneities are usually neglected. Here, we use the result from the recent concise derivation of the area distance in an inhomogeneous universe to study the monopole and Hubble residual of the apparent magnitude of Type Ia supernovae. We find that at low redshifts, the background FLRW spacetime model of the apparent magnitude receives corrections due to relative velocity perturbation in the observed redshift. We show how this velocity perturbation could contribute to a variance in the Hubble residual and how it could impact the calibration of the absolute magnitude of the Type Ia supernova in the Hubble flow. We also show that it could resolve the tension in the determination of the Hubble rate from the baryon acoustic oscillation and local measurements.