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.