Can interacting dark energy with dynamical coupling resolve the Hubble tension

The $H_0$ tension between low- and high- redshift measurements is definitely a serious issue faced by current cosmologists since it ranges from 4$\sigma$ to 6$\sigma$. To relieve this tension, in this paper we propose a new interacting dark energy model with time varying coupling parameter by parameterizing the densities of dark matter and dark energy, this parametric approach for interacting dark sectors are inspired by our previous work concerning the coupled generalized three-form dark energy model in which dark matter and dark energy behave like two uncoupled dark sectors with effective equation of state when the three-form $|\kappa X|\gg1$, for this reason, we reconstruct coupled generalized three-form dark energy from such parametric model under the condition $|\kappa X_0|\gg1$. In the end, we place constraints on three parametric models in light of the Planck 2018 cosmic microwave background (CMB) distance priors, baryon acoustic oscillations (BAO) data and the Pantheon compilation of Type Ia supernovae (SN Ia) data by assuming the parameter $k$ as 0,5,10 respectively. The fitting results show that, for all the observational data sets, the parametric models with $k=0,5,10$ relieve the Hubble tension with the latest local determinations of the Hubble constant from ${\rm SH_0ES}$ team, i.e. the so called R22, to 2.3 $\sigma$, 1.9 $\sigma$ and 1.3 $\sigma$ with $\chi_{\rm min}^2=10.43,10.47,10.48$ respectively, revealing that $k$ is positive correlated to the Hubble constant.