Novel approach toward the large-scale stable interacting dark-energy models and their astronomical bounds

Stability analysis of interacting dark-energy models generally divides its parameters space into two regions, (i) wₗ-1 and 0 and (ii) wₗ-1 and 0, where wₗ is the dark-energy equation of state and is the coupling strength of the interaction. Because of this separation, crucial information about the cosmology and phenomenology of these models may be lost. In a recent study, it has been shown that one can unify the two regions with a coupling function that depends on the dark-energy equation of state. In this work, we introduce a new coupling function that also unifies the two regions of the parameter space and generalizes the previous proposal. We analyze this scenario considering the equation of state of dark energy to be either constant or dynamical. We study the cosmology of such models and constrain both scenarios with the use of the latest astronomical data from both the background evolution as well as large-scale structures. Our analysis shows that a nonzero value of the coupling parameter as well as the dark-energy equation of state other than -1 are allowed. However, within 1 confidence level, =0 and the dark-energy equation of state equal to -1 are compatible with the current data. In other words, the observational data allow a very small but nonzero deviation from the cosmology; however, within the 1 confidence region, the interacting models can mimic the cosmology. In fact, we observe that the models both at the background and perturbative levels are very hard to distinguish from each other and from cosmology as well. Finally, we offer a rigorous analysis on the current tension on H₀, allowing different regions of the dark-energy equation of state, which shows that interacting dark-energy models reasonably solve the current tension on H₀.