  The LambdaCDM 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 sigma, 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 sigma. [...] Together with SNe Ia, more astrophysical probes
such as quasars (QSO) [...] and Gamma-Ray Bursts (GRBs) [...], are needed to
tackle the H0 tension. In the realm of GRB-cosmology, one of the most promising
correlations is the fundamental plane relation [...]. 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 Ibc that could be
exploited to standardize the class of GRB-SNe Ibc 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.
