Measurements of the luminosity distance of propagating gravitational waves can provide invaluable information on the geometry and content of our Universe. Due to the clustering of cosmic structures, in realistic situations we need to average the luminosity distance of events coming from patches inside a volume. In this work we evaluate, in a gauge-invariant and fully-relativistic treatment, the impact of cosmological perturbations on such averaging process. We find that clustering, lensing and peculiar velocity effects impact estimates for future detectors such as Einstein Telescope, Cosmic Explorer, the Big Bang Observer and DECIGO. The signal-to-noise ratio of the angular power spectrum of the average luminosity distance over all the redshift bins is 17 in the case of binary black holes detected by Einstein Telescope and Cosmic Explorer. We also provide fitting formulas for the corrections to the average luminosity distance due to general relativistic effects.

中文翻译：

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引力波光度 距离加权各向异性


测量传播引力波的光度距离可以提供有关我们宇宙的几何形状和内容的宝贵信息。由于宇宙结构的聚集，在现实情况下，我们需要平均来自体积内补丁的事件的光度距离。在这项工作中，我们以规范不变和完全相对论的处理方式评估了宇宙学扰动对这种平均过程的影响。我们发现，聚类、透镜和奇异的速度效应会影响对未来探测器的估计，例如爱因斯坦望远镜、宇宙探测器、大爆炸观察者和 DECIGO。在爱因斯坦望远镜和宇宙探测器探测到双黑洞的情况下，所有红移区间的平均光度距离的角功率谱的信噪比为 17。我们还提供了由于广义相对论效应而对平均光度距离进行校正的拟合公式。