Relieving the $H_0$ tension with a new interacting dark energy model

We investigate an extended cosmological model motivated by the asymptotic safety of gravitational field theory, in which the matter and radiation densities and the cosmological constant receive a correction parametrized by the parameters $\delta_G$ and $\delta_\Lambda$, leading to that both the evolutions of the matter and radiation densities and the cosmological constant slightly deviate from the standard forms. Here we explain this model as a scenario of vacuum energy interacting with matter and radiation. We consider two cases of the model: {(i) ${\tilde\Lambda}$CDM with one additional free parameter $\delta_G$, with $\delta_{\rm G}$ and $\delta_\Lambda$ related by a low-redshift limit relation and (ii) e${\tilde\Lambda}$CDM with two additional free parameters $\delta_G$ and $\delta_\Lambda$ that are independent of each other.} We use two data combinations, CMB+BAO+SN (CBS) and CMB+BAO+SN+$H_0$ (CBSH), to constrain the models. We find that, in the case of using the CBS data, neither ${\tilde\Lambda}$CDM nor e${\tilde\Lambda}$CDM can effectively alleviate the $H_0$ tension. However, it is found that using the CBSH data the $H_0$ tension can be greatly relieved by the models. In particular, in the case of e${\tilde\Lambda}$CDM, the $H_0$ tension can be resolved to 0.71$\sigma$. We conclude that as an interacting dark energy model, ${\tilde\Lambda}$CDM is much better than $\Lambda(t)$CDM in the sense of both relieving the $H_0$ tension and fitting to the current observational data.