H_0 tension or M overestimation?

Abstract

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 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 (Wong et al. in The local hole: a galaxy under-density covering 90 mpc, 2021).