The standard cosmological model, the ΛCDM 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 (𝐻0) tension, namely, the difference of about
5𝜎 as an average between the value of 𝐻0 estimated locally and the cosmological value measured
from the Last Scattering Surface. The value of this tension changes from 4 to 6 𝜎 according to
the data used. The current analysis explores the 𝐻0 tension in the Pantheon sample (PS) of SNe
Ia. Through the division of the PS in 3 and 4 bins, the value of 𝐻0 is estimated for each bin and
all the values are fitted with a decreasing function of the redshift (𝑧). Remarkably, 𝐻0 undergoes
a slow decreasing evolution with 𝑧, having an evolutionary coefficient compatible with zero up
to 5.8𝜎. 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.