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.
