On the Hubble constant tension in the SNe Ia Pantheon sample

The Hubble constant ($H_0$) tension between Type Ia Supernovae (SNe Ia) and Planck measurements ranges from 4 to 6 $\sigma$. To investigate this tension, we estimate $H_{0}$ in the $\Lambda$CDM and $w_{0}w_{a}$CDM models by dividing the Pantheon sample, the largest compilation of SNe Ia, into 3, 4, 20 and 40 bins. We fit the extracted $H_{0}$ values with a function mimicking the redshift evolution: $g(z)={H_0}(z)=\tilde{H}_0/(1+z)^\alpha$, where $\alpha$ indicates an evolutionary parameter and $\tilde{H}_0=H_0$ at $z=0$. We set the absolute magnitude of SNe Ia so that $H_0=73.5\,\, \textrm{km s}^{-1}\,\textrm{Mpc}^{-1}$, and we fix fiducial values for $\Omega_{0m}^{\Lambda CDM}=0.298$ and $\Omega_{0m}^{w_{0}w_{a}CDM}=0.308$. We find that $H_0$ evolves with redshift, showing a slowly decreasing trend, with $\alpha$ coefficients consistent with zero only from 1.2 to 2.0 $\sigma$. Although the $\alpha$ coefficients are compatible with 0 in 3 $\sigma$, this however may affect cosmological results. We measure locally a variation of $H_0(z=0)-H_0(z=1)=0.4\, \textrm{km s}^{-1}\,\textrm{Mpc}^{-1}$ in 3 and 4 bins. Extrapolating ${H_0}(z)$ to $z=1100$, the redshift of the last scattering surface, we obtain values of $H_0$ compatible in 1 $\sigma$ with Planck measurements independently of cosmological models and number of bins we investigated. Thus, we have reduced the $H_0$ tension from $54\%$ to $72\%$ for the $\Lambda$CDM and $w_{0}w_{a}$CDM models, respectively. If the decreasing trend of $H_0(z)$ is real, it could be due to astrophysical selection effects or to modified gravity.