Quantifying the impacts of future gravitational-wave data on
  constraining interacting dark energy
  In this work, we investigate the impacts of the future gravitational-wave
(GW) standard siren observation by the Einstein Telescope (ET) on constraining
the interacting dark energy (IDE) models. We simulate 1000 GW events in the
redshift range of $0\lesssim z \lesssim 5$ based on the 10-year observation of
the ET. We combine the simulated GW data with the current mainstream
cosmological electromagnetic observations including the cosmic microwave
background anisotropies, the baryon acoustic oscillations, and the type Ia
supernovae to constrain the IDE models. We consider typical IDE models in the
context of a perturbed universe. To avoid the large-scale instability problem
for IDE models, we apply the extended parameterized post-Friedmann approach to
calculate the cosmological perturbations. We find that the addition of the GW
standard siren data could significantly improve the constraint accuracies for
most of the cosmological parameters (e.g., $H_{0}$, $w$, and $\Omega_{\rm m}$).
For the coupling parameter $\beta$, the constraint errors could also be
slightly improved when adding the GW data in the cosmological fit.
