Constraints on interacting dark energy model from lensed quasars: Relieving the $H_0$ tension from 5.3$σ$ to 1.7$σ$

Measurements for strong gravitational lensing time delays between multiple images of background quasars can provide an independent probe to explore the expansion history of the late-time universe. In this paper, we employ the new results of the time-delay (TD) measurements for six strong gravitational lens systems to constrain interacting dark energy (IDE) model. We mainly focus on the model of vacuum energy (with $w=-1$) interacting with cold dark matter, and consider four typical cases of the interaction form. Our main findings include: (i) the IDE models with $Q\propto \rho_{\rm de}$ have an advantage in alleviating the $H_{0}$ tension between the cosmic microwave background and TD observations; (ii) when the TD data are combined with the latest local distance-ladder result, the $H_0$ tension can be alleviated from $5.3\sigma$ (in the standard $\Lambda$CDM cosmology) to $1.7\sigma$ in the IDE model with the interaction term $Q=\beta H\rho_{\rm de}$; (iii) the coupling parameter $\beta$ in all the considered IDE models are preferred to be positive around 1$\sigma$ range when the late-universe measurements (TD+SN) are used to perform constraint, implying a mild preference for the case of cold dark matter decaying into dark energy by the late-universe observations.