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.
