标题： 使用下一代引力波探测器的主成分分析进行广义相对论的多参数检验 显示英文标题

标题： Multiparameter tests of general relativity using principal component analysis with next-generation gravitational wave detectors

摘要： 主成分分析（PCA）是一种有效的工具，用于优化广义相对论（GR）的多参数测试，在这种测试中，通过引入分数变形参数来同时测试多个后牛顿（PN）相位系数的偏差。我们使用PCA从数据中构建“最佳测量”的PN变形参数的线性组合。这有助于对GR的偏差设置严格的限制并检测可能的超出GR的物理现象。在本文中，我们研究了这种方法在 proposed 的下一代引力波探测器——宇宙探索者（CE）和爱因斯坦望远镜（ET）中的有效性。在探测器框架中，总质量在20-200 $\mathrm{M}_{\odot}$之间的致密双星系统，在光度距离为500 Mpc的情况下，CE可以以优于10%的精度测量三个最主要的线性组合，并以优于0.1%的精度测量最主要的线性组合。对于特定的质量范围和线性组合，ET的约束比CE好几个数量级。这种改进是因为ET相比CE在1-5 Hz频率范围内的低频灵敏度得到了提高。此外，我们解释了PCA参数对不同PN变形参数的灵敏度，并讨论了它们随总质量的变化情况。我们还讨论了一个用于量化捕获信号信息的最主要线性组合数量的准则。 显示英文摘要

摘要： Principal Component Analysis (PCA) is an efficient tool to optimize the multiparameter tests of general relativity (GR) where one tests for simultaneous deviations in multiple post-Newtonian (PN) phasing coefficients by introducing fractional deformation parameters. We use PCA to construct the `best-measured' linear combinations of the PN deformation parameters from the data. This helps to set stringent limits on deviations from GR and detect possible beyond-GR physics. In this paper, we study the effectiveness of this method with the proposed next-generation gravitational wave detectors, Cosmic Explorer (CE) and Einstein Telescope (ET). Observation of compact binaries with total masses between 20-200 $\mathrm{M}_{\odot}$ in the detector frame and at a luminosity distance of 500 Mpc, CE can measure the three most dominant linear combinations to an accuracy better than 10%, and the most dominant one to better than 0.1%. For specific ranges of masses and linear combinations, constraints from ET are better by a few factors than CE. This improvement is because of the improved low frequency sensitivity of ET compared to CE (between 1-5 Hz). In addition, we explain the sensitivity of the PCA parameters to the different PN deformation parameters and discuss their variation with total mass. We also discuss a criterion for quantifying the number of most dominant linear combinations that capture the information in the signal up to a threshold.