Uncertainty and Bias of Cosmology and Astrophysical Population Model from Statistical Dark Sirens
Uncertainty and Bias of Cosmology and Astrophysical Population Model from Statistical Dark Sirens
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DOI：
10.3847/1538-4357/ac9da0
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发表时间：
2022-06
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影响因子：
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通讯作者：
Hang Yu;Brian C Seymour;Yijun Wang;Yanbei Chen
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作者：
Hang Yu;Brian C Seymour;Yijun Wang;Yanbei Chen
来自凝聚的致密双星的引力波(GW)辐射是一个标准的警报器，因为每个事件的光度距离可以从信号的幅度直接测量。使用GW警报器约束宇宙学的一种可能性是对一组双黑洞(BBH)事件进行统计推断。从本质上讲，这种统计方法可以被认为是如下的。我们可以通过改变宇宙学参数来修改观测到的BBH事件分布的形状，直到它最终与由天体物理人口模型构建的分布相匹配，从而允许我们确定宇宙学参数。在这项工作中，我们通过检查事件分布中包含的Fisher信息，从这种统计暗警报方法中推导出宇宙学参数和支配天体物理人口模型的参数的Cramér-Rao界。我们的研究提供了分析洞察力，并能够快速而准确地估计暗海妖宇宙学的统计准确性。此外，我们还考虑了由于合并率和质量分布中未模型化的子结构而导致的宇宙学偏差。我们发现，天体物理模型中1%的偏差可以导致哈勃常数的误差超过1%。当探测到超过104个BBH事件时，这可能会限制暗警报宇宙学的准确性。
Gravitational-wave (GW) radiation from a coalescing compact binary is a standard siren, as the luminosity distance of each event can be directly measured from the amplitude of the signal. One possibility to constrain cosmology using the GW siren is to perform statistical inference on a population of binary black hole (BBH) events. In essence, this statistical method can be viewed as follows. We can modify the shape of the distribution of observed BBH events by changing the cosmological parameters until it eventually matches the distribution constructed from an astrophysical population model, thereby allowing us to determine the cosmological parameters. In this work, we derive the Cramér–Rao bound for both cosmological parameters and those governing the astrophysical population model from this statistical dark siren method by examining the Fisher information contained in the event distribution. Our study provides analytical insights and enables fast yet accurate estimations of the statistical accuracy of dark siren cosmology. Furthermore, we consider the bias in cosmology due to unmodeled substructures in the merger rate and mass distribution. We find that a 1% deviation in the astrophysical model can lead to a more than 1% error in the Hubble constant. This could limit the accuracy of dark siren cosmology when there are more than 104 BBH events detected.