$H_0$ tension or $M$ overestimation?

Abstract: There is a strong discrepancy between the value of the Hubble parameter $H_0<sup>P$ obtained from large scale observations such as the Planck mission, and the small scale value $H_0<sup>R$, obtained from low redshift supernovae (SNe). The value of the absolute magnitude $M<sup>{Hom}$ used as prior in analyzing observational data is obtained from low-redshift SNe, assuming a homogeneous Universe, but the distance of the anchors used to calibrate the SNe to obtain $M$ would be affected by a local inhomogeneity, making it inconsistent to test the Copernican principle using $M<sup>{Hom}$, since $M$ estimation itself is affected by local inhomogeneities. We perform an analysis of the luminosity distance of low redshift SNe, using different values of $M$, ${M<sup>P,M<sup>R}$, corresponding to different values of $H_0$, ${H_0<sup>P,H_0<sup>R}$, obtained from the model independent consistency relation between $H_0$ and $M$ which can be derived from the definition of the distance modulus. We find that the value of $M$ can strongly affect the evidence of a local inhomogeneity. We analyze data from the Pantheon catalog, finding no significant statistical evidence of a local inhomogeneity using the parameters ${M<sup>R,H_0<sup>R}$, confirming previous studies, while with ${M<sup>P,H_0<sup>P}$ we find evidence of a small local void, which causes an overestimation of $M<sup>R$ with respect to $M<sup>P$. An inhomogeneous model with the parameters ${M<sup>P,H_0<sup>P}$ fits the data better than a homogeneous model with ${M<sup>R,H_0<sup>R}$, resolving the apparent $H_0$ tension. Using ${M<sup>P,H_0<sup>P}$, we obtain evidence of a local inhomogeneity with a density contrast $-0.140 \pm 0.042$, extending up to a redshift of $z_v =0.056 \pm 0.0002$, in good agreement with recent results of galaxy catalogs analysis.