Shedding new light on the Hubble constant tension through Supernovae Ia

The standard cosmological model, the $\mathrm{\Lambda }$CDM model, is the most suitable description for our universe. This framework can explain the accelerated expansion phase of the universe but still is not immune to open problems when it comes to the comparison with observations. One of the most critical issues is the so-called Hubble constant ($H_0$) tension, namely, the difference of about $5\sigma$ as an average between the value of $H_0$ estimated locally and the cosmological value measured from the Last Scattering Surface. The value of this tension changes from 4 to 6 $\sigma$ according to the data used. The current analysis explores the $H_0$ tension in the $\mathit{\text{Pantheon}}$ sample (PS) of SNe Ia. Through the division of the PS in 3 and 4 bins, the value of $H_0$ is estimated for each bin and all the values are fitted with a decreasing function of the redshift ($z$). Remarkably, $H_0$ undergoes a slow decreasing evolution with $z$, having an evolutionary coefficient compatible with zero up to $5.8\sigma$. If this trend is not caused by hidden astrophysical biases or $z$-selection effects, then the $f(R)$ modified theories of gravity represent a valid model for explaining such a trend.