Novel approach towards 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) $w_x \geq -1$ and $\xi \geq 0$ and (ii) $w_x \leq -1$ and $\xi \leq 0$, where $w_x$ is the dark energy equation of state and $\xi$ is the coupling strength of the interaction. Due to 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 which depends on the dark energy equation of state. In this work we introduce a new coupling function which also unifies the two regions of the parameter space and generalises the previous proposal. We analyse this scenario considering the equation of state of DE to be either constant or dynamical. We study the cosmology of such models and constrain both scenarios with the use of latest astronomical data from both background evolution as well as large scale structures. Our analysis shows that a non-zero value of the coupling parameter $\xi$ as well as the dark energy equation of state other than `$-1$' are allowed. However, within $1\sigma$ confidence level, $\xi = 0$, 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 $\Lambda$-cosmology, however, within $1\sigma$ confidence-region the interacting models can mimick the $\Lambda$-cosmology. In fact we observe that the models both at background and perturbative levels are very hard to distinguish form each other and from $\Lambda$-cosmology as well. Finally, we offer a rigorous analysis on the current tension on $H_0$ allowing different regions of the dark energy equation of state which shows that interacting dark energy models reasonably solve the current tension on $H_0$.