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.

中文翻译：

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量化未来引力波数据对约束相互作用暗能量的影响

在这项工作中，我们研究了爱因斯坦望远镜 (ET) 未来引力波 (GW) 标准警报器观测对约束相互作用暗能量 (IDE) 模型的影响。我们基于对 ET 的 10 年观察，在 $0\lesssim z \lesssim 5$ 的红移范围内模拟了 1000 GW 事件。我们将模拟的 GW 数据与当前主流的宇宙学电磁观测结合起来，包括宇宙微波背景各向异性、重子声学振荡和 Ia 型超新星来约束 IDE 模型。我们在扰动宇宙的背景下考虑典型的 IDE 模型。为了避免 IDE 模型的大规模不稳定问题，我们应用扩展的参数化后弗里德曼方法来计算宇宙学扰动。我们发现添加 GW 标准警报器数据可以显着提高大多数宇宙学参数（例如，$H_{0}$、$w$ 和 $\Omega_{\rm m}$）的约束精度。对于耦合参数 $\beta$，在宇宙拟合中加入 GW 数据时，约束误差也可以略有改善。