New parametrization of the dark-energy equation of state with a single parameter

We propose a novel dark-energy equation-of-state parametrization, with a single parameter $\eta$ that quantifies the deviation from $\Lambda$CDM cosmology. We first confront the scenario with various datasets, from Hubble function (OHD), Pantheon, baryon acoustic oscillations (BAO), and their joint observations, and we show that $\eta$ has a preference for a non-zero value, namely a deviation from $\Lambda$CDM cosmology is favored, although the zero value is marginally inside the 1$\sigma$ confidence level. However, we find that the present Hubble function value acquires a higher value, namely $H_0= 66.624^{+0.011}_{-0.013}~Km~ s^{-1} Mpc^{-1}$, which implies that the $H_0$ tension can be partially alleviated. Additionally, we perform a cosmographic analysis, showing that the universe transits from deceleration to acceleration in the recent cosmological past, nevertheless, in the future, it will not result in a de Sitter phase, since it exhibits a second transition from acceleration to deceleration. Finally, we perform the Statefinder analysis. The scenario behaves similarly to the $\Lambda$CDM paradigm at high redshifts, while the deviation becomes significant at late and recent times and especially in the future.