We present a detailed exposition of a statistical method for estimating cosmological parameters from the observation of a large number of strongly lensed binary-black-hole (BBH) mergers observable by next (third) generation (XG) gravitational-wave (GW) detectors. This method, first presented in Jana (2023 Phys. Rev. Lett. 130 261401), compares the observed number of strongly lensed GW events and their time delay distribution (between lensed images) with observed events to infer cosmological parameters. We show that the precision of the estimation of the cosmological parameters does not have a strong dependance on the assumed BBH redshift distribution model. Using the large number of unlensed mergers, XG detectors are expected to measure the BBH redshift distribution with sufficient precision for the cosmological inference. However, a biased inference of the BBH redshift distribution will bias the estimation of cosmological parameters. An incorrect model for the distribution of lens properties can also lead to a biased cosmological inference. However, Bayesian model selection can assist in selecting the right model from a set of available parametric models for the lens distribution. We also present a way to incorporate the effect of contamination in the data due to the limited efficiency of lensing identification methods, so that it will not bias the cosmological inference.

中文翻译：

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使用第三代引力波探测器的强透镜宇宙学


我们详细阐述了一种统计方法，该方法通过观察下一代（第三代）引力波 （GW） 探测器可观察到的大量强透镜双黑洞 （BBH） 合并来估计宇宙学参数。这种方法首次在 Jana （2023 Phys. Rev. Lett.130 261401） 中提出，将观察到的强透镜 GW 事件的数量及其时间延迟分布（在透镜图像之间）与观测事件进行比较，以推断宇宙学参数。我们表明，宇宙学参数估计的精度对假设的 BBH 红移分布模型没有很强的依赖性。利用大量未聚焦的合并，XG 探测器有望以足够的精度测量 BBH 红移分布以进行宇宙学推断。然而，对 BBH 红移分布的偏倚推断将使宇宙学参数的估计产生偏差。不正确的透镜属性分布模型也可能导致有偏差的宇宙学推断。但是，贝叶斯模型选择可以帮助从一组可用的参数模型中为透镜分布选择正确的模型。由于透镜识别方法的效率有限，我们还提出了一种将污染的影响纳入数据的方法，这样它就不会使宇宙学推断产生偏差。