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 is 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 is 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) all the considered IDE models aggravate the
$\sigma_8$ tension, while the $S_8$ tension could be slightly relieved in the
IDE model with $Q = \beta H_{0} \rho_{\rm c}$; (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 is employed, and none of them
can achieve good scores in all aspects.
