Dynamical analysis of the H^2 + H^-2 Dark Energy model considering viscosity and interaction

In this study, we further developed and investigated the dual parameter phenomenological dark energy model (H^2 + H^-2 dark energy model) derived from Kaniadakis holographic dark energy. On the theoretical basis of the original H^2 + H^-2 dark energy model (HHDE), four types of viscosities and seven types of interactions were introduced. These were combined pairwise, and a dynamical analysis was conducted on a total of 35 Modified H^2 + H^-2 Viscous Interacting Dark Energy (MHH-VIDE) models. The advantage of the HHDE model and MHH-VIDE models is that these models can greatly relieve the Hubble tension and cicumventing the potential issue of a 'big rip', and the dark energy is Quintom-like. In this article, we performed a three-dimensional dynamical analysis of the aforementioned models with interactions and viscosity, testing their viability. The results suggest that the nature of this dark energy is closer to a property of spacetime than a cosmological component. The phase diagram analysis reveals a modified radiation-dominated epoch, a transitional matter-dominated phase, and a late-time attractor corresponding to the dark-energy-driven acceleration phase.