A New Master Supernovae Ia sample and the investigation of the H_0 tension

We present a cosmological analysis of the Hubble constant using the largest homogenized sample of Type Ia Supernovae (SNe) currently available, consisting of 3714 events compiled from the Pantheon, Pantheon+, JLA, and DES catalogues. By applying several redshift-binning techniques and performing Markov Chain Monte Carlo analyses within the flat $\Lambda$CDM and $w_0 w_a$ CDM cosmological models, we investigate the possible redshift dependence of the Hubble parameter $H_0 (z)$. The results reveal a mild decreasing trend of the Hubble parameter with increasing redshift, described by the phenomenological relation $H_0 (z)= \tilde{H}_0/(1+z)^\alpha$, where $\tilde{H}_0$ represents the local value and $\alpha$ quantifies the evolutionary behaviour. We find $\alpha \sim 0.01$, with the statistical significance varying across different binning configurations and reaching values above $3 \sigma$ in several cases. These results are robust against variations in binning methods, cosmological models, and supernova subsamples, suggesting that the observed behaviour may reflect either astrophysical evolution or underlying cosmological effects. We discuss two new physical theoretical models discussing this data trend and compare them with the power law behaviour