Observational constraints of a new unified dark fluid and the $H_0$ tension

Abstract: Unified cosmological models have received a lot of attention in astrophysics community for explaining both the dark matter and dark energy evolution. The Chaplygin cosmologies, a well known name in this group have been investigated matched with observations from different sources. Obviously, Chaplygin cosmologies have to obey restrictions in order to be consistent with the observational data. As a consequence, alternative unified models, differing from Chaplygin model, are of special interest. In the present work we consider a specific example of such a unified cosmological model, that is quantified by only a single parameter $\mu$, that can be considered as a minimal extension of the $\Lambda$-cold dark matter cosmology. We investigate its observational boundaries together with an analysis of the universe at large scale. Our study shows that at early time the model behaves like a dust, and as time evolves, it mimics a dark energy fluid depicting a clear transition from the early decelerating phase to the late cosmic accelerating phase. Finally, the model approaches the cosmological constant boundary in an asymptotic manner. We remark that for the present unified model, the estimations of $H_0$ are slightly higher than its local estimation and thus alleviating the $H_0$ tension.