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

Modern cosmological research still thoroughly debates the discrepancy between local probes and the Cosmic Microwave Background observations in the Hubble constant ($H_0$) measurements, ranging from 4 to 6σ. In the current study, we examine this tension using the Supernovae Ia (SNe Ia) data from the Pantheon, Pantheon+ (P+), Joint Lightcurve Analysis (JLA), and Dark Energy Survey, (DES) catalogs combined together into the so-called Master Sample. The sample contains 3714 SNe Ia, and is divided all of them into redshift-ordered bins. Three binning techniques are presented: the equi-population, the moving window (MW), and the equi-spacing in the $\log -z$. We perform a Markov-Chain Monte Carlo analysis (MCMC) for each bin to determine the $H_0$ value, estimating it within the standard flat ΛCDM and the $w_0{w}_a$CDM models. These $H_0$ values are then fitted with the following phenomenological function: $H_0\left(z\right)={\tilde{H}}_0/{(1+z)}^{\alpha }$, where ${\tilde{H}}_0$ is a free parameter representing $H_0\left(z\right)$ fitted in $z=0$, and α is the evolutionary parameter. Our results indicate a decreasing trend characterized by $\alpha \sim 0.01$, whose consistency with zero ranges from 1σ in 5 cases to 1 case at 3 σ and 11 cases at $>3\sigma$ in several samples and configurations. Such a trend in the SNe Ia catalogs could be due to evolution with redshift for the astrophysical variables or unveiled selection biases. Alternatively, intrinsic physics, possibly the $f\left(R\right)$ theory of gravity, could be responsible for this trend.