The ΛCDM model is the most commonly accepted framework in modern cosmology. However, the
local measurements of the Hubble constant, 𝐻0, via the Supernovae Type Ia (SNe Ia) calibrated on
Cepheids provide a value which is in significant disagreement, from 4 to 6 𝜎, with the value of 𝐻0
inferred from the Cosmic Microwave Background (CMB) observed by Planck. This disagreement
is the so-called Hubble constant tension. To find out the reason for this discrepancy, we analyze
the behaviour of the 𝐻0 in the Pantheon sample of SNe Ia through a binning approach: we divide
the Pantheon into 3 and 4 bins ordered with redshift (𝑧), and for each of them, we estimate the
𝐻0. After the 𝐻0 estimation, we fit the 𝐻0 values with a decreasing function of 𝑧, finding out that
𝐻0 undergoes a slow decreasing trend compatible with the evolution scenario in 2.0 𝜎. Such a
behaviour could be explained by hidden astrophysical biases or the evolution with 𝑧 for the SNe
Ia parameters. If not, the 𝑓 (𝑅) modified gravity theories could be invoked to alleviate or solve
the 𝐻0 tension. Together with SNe Ia, more astrophysical probes, which are much more distant
than SNe Ia, are needed to tackle the 𝐻0 tension. In this perspective, the Gamma-Ray Bursts
(GRBs) come to aid. In the realm of GRB-cosmology, one of the most promising correlations is
the fundamental plane relation, which is among the luminosity at the end of the plateau emission,
its rest-frame duration, and the peak prompt luminosity [10–12]. In the context of applying this
relation as a cosmological tool, we also compute how many GRBs must be gathered to reach
the same precision as the SNe Ia. Since we are about two decades away from reaching such
precision, we also attempt to find additional correlations for the GRBs associated with SNe Ib/c
that could be exploited to standardize the class of GRB-SNe Ib/c in the future. We find a hint of
a correlation between the GRBs’ end-of-plateau optical luminosity and the SNe’s rest-frame peak
time, suggesting that the GRBs with the most luminous optical plateau emission are associated
with SNe with the most delayed peaks in their light curves. So far, it is the fundamental plane
relation to be the most promising candle for exploring the high-𝑧 universe