H${}_0$ tension or M overestimation?

There is a strong discrepancy between the value of the Hubble parameter H${}_0^P$ obtained from large scale observations such as the Planck mission, and the small scale value H${}_0^R$, obtained from low redshift supernovae (SNe). The value of the absolute magnitude M${}^{Hom}$ 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${}^{Hom}$, 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${}^P$, M${}^R$}, corresponding to different values of H${}_0$, {H${}_0^P$, H${}_0^R$}, 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${}^R$, H${}_0^R$}, confirming previous studies, while with {M${}^P$, H${}_0^P$} we find evidence of a small local void, which causes an overestimation of M${}^R$ with respect to M${}^P$. An inhomogeneous model with the parameters {M${}^P$, H${}_0^P$} fits the data better than a homogeneous model with {M${}^R$, H${}_0^R$}, resolving the apparent H${}_0$ tension. Using {M${}^P$, H${}_0^P$}, we obtain evidence of a local inhomogeneity with a density contrast -0.140 ± 0.042, extending up to a redshift of $z_v$ = 0.056 ± 0.0002, in good agreement with recent results of galaxy catalogs analysis (Wong et al. in The local hole: a galaxy under-density covering 90 mpc, 2021).