We use gravitational wave (GW) standard sirens, in addition to Type Ia supernovae (SNIa) and baryon acoustic oscillation (BAO) mock data, to forecast constraints on the electromagnetic and gravitational distance duality relations (DDR). We make use of a parameterised approach based on a specific DDR violation model, along with a machine learning reconstruction method based on the Genetic Algorithms. We find that GW provide an alternative to the use of BAO data to constrain violations of the DDR, reaching $3\%$ constraints on the violation parameter we consider when combined with SNIa, which is only improved by a factor of $\approx1.4$ if one instead considers the combination of BAO and SNIa. We also investigate the possibility that a neglected modification of gravity might lead to a false detection of DDR violations, even when screening mechanisms are active. We find that such a false detection can be extremely significant, up to $\approx10\sigma$ for very extreme modified gravity scenarios, while this reduces to $\approx4\sigma$ in a more realistic case. False detections can also provide a smoking gun for the modified gravity mechanism at play, as a result of the tension introduced between the SNIa+GW and SNIa+BAO combinations.

中文翻译：

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对标准警报器距离对偶关系的约束

除了 Ia 型超新星 (SNIa) 和重子声波振荡 (BAO) 模拟数据外，我们还使用引力波 (GW) 标准警报器来预测对电磁和引力距离对偶关系 (DDR) 的约束。我们使用基于特定 DDR 违规模型的参数化方法，以及基于遗传算法的机器学习重建方法。我们发现 GW 提供了一种替代使用 BAO 数据来约束 DDR 违规的方法，当与 SNIa 结合时，我们考虑的违规参数达到 $3\%$ 约束，仅提高了 $\approx1.4 $ 如果转而考虑 BAO 和 SNIa 的组合。我们还调查了忽略重力修改可能导致错误检测 DDR 违规的可能性，即使筛选机制处于活动状态。我们发现这样的错误检测可能非常显着，对于非常极端的修改重力场景高达 $\approx10\sigma$，而在更现实的情况下这减少到 $\approx4\sigma$。由于在 SNIa+GW 和 SNIa+BAO 组合之间引入了张力，错误检测还可以为改进的重力机制提供证据。