# Exploring the evidence for a large local void with supernovae Ia data

## TL;DR

This study uses recent supernova data and a Lemaître-Tolman-Bondi cosmological model to investigate large local inhomogeneities, finding a small local void unlikely to explain the H0 tension but possibly contributing to systematic errors.

## Contribution

It provides new constraints on local void size and density contrast using SN Ia data within a $
m \Lambda$LTB framework, and compares these with luminosity density data.

## Key findings

- Local void size estimated at z=0.068 with significant uncertainty
- Large local inhomogeneity unlikely to resolve H0 tension alone
- SN Ia data suggest a systematic error of about 1.1% in H0 measurements

## Abstract

In this work we utilise the most recent publicly available type Ia supernova (SN Ia) compilations and implement a well formulated cosmological model based on Lema\^{i}tre-Tolman-Bondi metric in presence of cosmological constant $\Lambda$ ($\Lambda$LTB) to test for signatures of large local inhomogeneities at $z\leq0.15$. Local underdensities in this redshift range have been previously found based on luminosity density (LD) data and galaxy number counts. Our main constraints on the possible local void using the Pantheon SN Ia dataset are: redshift size of $z_{\rm size}=0.068^{+0.021}_{-0.030}$; density contrast of $\delta\Omega_0/\Omega_0=-10.5_{-7.4}^{+9.3}\%$ between 16th and 84th percentiles. Investigating the possibility to alleviate the $\sim9\%$ disagreement between measurements of present expansion rate $H_0$ coming from calibrated local SN Ia and high-$z$ cosmic microwave background data, we find large local void to be a very unlikely explanation alone, consistently with previous studies. However, the level of matter inhomogeneity at a scale of $\sim$100Mpc that is allowed by SN Ia data, although not expected from cosmic variance calculations in standard model of cosmology, could be the origin of additonal systematic error in distance ladder measurements based on SN Ia. Fitting low-redshift Pantheon data with a cut $0.023<z<0.15$ to the $\Lambda$LTB model and to the Taylor expanded luminosity distance formula we estimate that this systematic error amounts to $1.1\%$ towards the lower $H_0$ value. A test for local anisotropy in Pantheon SN Ia data yields null evidence. Analysis of LD data provides a constraint on contrast of large isotropic void $\delta\Omega_0/\Omega_0=-51.9\%\pm6.3\%$, which is in $\sim4\sigma$ tension with SN Ia results. More data are necessary to better constrain the local matter density profile and understand the disagreement between SN and LD samples