Constraints on interacting dark energy models from time-delay cosmography with seven lensed quasars

Measurements of time-delay cosmography of lensed quasars can provide an independent probe to explore the expansion history of the late-time Universe. In this paper, we employ the time-delay cosmography measurements from seven lenses (here abbreviated as the TD data) to constrain interacting dark energy (IDE) models. We mainly focus on the scenario of vacuum energy (with $w=-1$) interacting with cold dark matter, and consider four typical cases of the interaction form $Q$. When the TD data alone are employed, we find that the IDE models with $Q\propto \rho_{\rm de}$ seem to have an advantage in relieving the $H_{0}$ tension between the cosmic microwave background (CMB) and TD data. When the TD data are added to the CMB$+$BAO$+$SN$+H_0$ data, we find that: (i) the coupling parameter $\beta$ in all the considered IDE models is positive within 1$\sigma$ range, implying a mild preference for the case of cold dark matter decaying into dark energy; (ii) the IDE model with $Q = \beta H_{0} \rho_{\rm c}$ slightly relieves the $S_8$ tension, but the other considered IDE models further aggravate this tension; (iii) the Akaike information criteria of the IDE models with $Q \propto \rho_{\rm c}$ are lower than that of the $\Lambda$CDM model, indicating that these IDE models are more preferred by the current mainstream data. We conclude that the considered IDE models have their own different advantages when the TD data are employed, and none of them can achieve good scores in all aspects.