Bayesian analysis of a Unified Dark Matter model with transition: can it alleviate the $H_{0}$ tension?

We consider cosmological models in which Dark Matter (DM) and Dark Energy (DE) are described by a single component, dubbed Unified Dark Matter (UDM) models, in which the DE-like part can have an equation state $<-1$ at late times without violating the null energy condition. In this paper, we investigate whether this feature can relieve the Hubble tension. We perform a Bayesian analysis of the model using SNIa data from Pantheon, the CMB distance prior from Planck, and the prior on the absolute magnitude $M$ of SNIa from SH0ES. Using the prior, the data suggests a smooth transition taking place at redshifts $z_{\rm t} \simeq 2.85$, which provides a value $H_0=69.64\pm 0.88$ for the Hubble constant, slightly alleviating the tension by $\sim 1.5 \sigma$. Without it, we obtain $H_0 = 67.6^{+1.3}_{-0.82}$ and a transition happening at $z_t=1.36$. We also discuss the importance of using the prior on $M$ for constraining this model.