Exploration of interacting dynamical dark energy model with interaction term including the equation-of-state parameter: alleviation of the H₀ tension

We explore a scenario of interacting dynamical dark energy model with the interaction term $Q$ including varying equation-of-state parameter $w$. Using data combination cosmic microwave background, baryon acoustic oscillation, and type Ia supernovae, to global fit model, we find that adding factor $w$ in function can change correlations between coupling constant $\beta$ other parameters, then has huge impact on fitting result $\beta$. In this value $H_{0}$ is lower at $3.54 \sigma$ level than direct measurement . Comparing case excluding $w$, more favored by current mainstream observation. To obtain higher values narrow discrepancy different observations, additional parameters effective number relativistic species, total neutrino mass, massive sterile neutrinos are considered cosmology. tension be further reduced these models, but still about $3 level.