# The Local Perspective on the Hubble Tension: Local Structure Does Not Impact Measurement of the Hubble Constant

## TL;DR

This study uses extensive supernova data to show that local cosmic structures do not significantly influence Hubble constant measurements, supporting the robustness of current distance ladder methods against local density variations.

## Contribution

It provides the most comprehensive analysis to date demonstrating that local voids do not impact Hubble constant estimates, reinforcing the reliability of the distance ladder approach.

## Key findings

- Large local underdensities are inconsistent with SN Ia data at 4-5 sigma.
- No evidence of local density effects on Hubble constant within 0.023<z<0.15.
- Distance measurements remain precise despite local structure uncertainties.

## Abstract

We use the largest sample to date of spectroscopic SN Ia distances and redshifts to look for evidence in the Hubble diagram of large scale outflows caused by local voids suggested to exist at z<0.15. Our sample combines data from the Pantheon sample with the Foundation survey and the most recent release of lightcurves from the Carnegie Supernova Project to create a sample of 1295 SNe over a redshift range of 0.01<z<2.26. We make use of an inhomogeneous and isotropic Lemaitre-Tolman-Bondi metric to model a void in the SN Ia distance-redshift relation. We conclude that the SN luminosity distance-redshift relation is inconsistent at the 4-5 sigma confidence level with large local underdensities (|delta| > 20%, where the density contrast delta = Delta rho /rho) proposed in some galaxy count studies, and find no evidence of a change in the Hubble constant corresponding to a void with a sharp edge in the redshift range 0.023<z<0.15. With empirical precision of sigma_H_0 = 0.60%, we conclude that the distance ladder measurement is not affected by local density contrasts, in agreement with cosmic variance of sigma_H_0 = 0.42% predicted from simulations of large-scale structure. Given that uncertainty in the distance ladder value is sigma_H_0=2.2%, this does not affect the Hubble tension. We derive a 5 sigma constraint on local density contrasts on scales larger than 69 megaparsec h^-1 of delta < 27%. The presence of local structure does not appear to impede the possibility of measuring the Hubble constant to 1% precision.