修正引力波传播的O5暗警报预测：$Ξ$后验的背景稳健性
O5 dark-siren forecasts for modified GW propagation: background robustness of the $Ξ$ posterior
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中文总结 AI 辅助
研究双黑洞合并暗警报中$\Xi$后验的背景稳健性，通过分析无星系目录的O5模拟事件，改变$\Omega_m$比较不同推断方法，发现边缘化$\Xi$后验在此区间不变，联合推断有相关结果，且即使暗警报主导检测率，高精度$\Xi$测试仍需测量红移。
中文摘要 AI 辅助
预计无电磁对应体的双黑洞合并将在O5引力波目录中占主导地位。近期CHIMERA~2.0预测通常将$\Omega_m$固定为CMB告知的值，并在可用时使用光谱宿主，但尚未针对公共O5模拟目录中的纯暗警报评估$\Xi$后验的相应灵敏度。我们分析了300个无星系目录的O5灵敏度模拟事件，在$[0.20,\,0.35]$范围内改变$\Omega_m$（包括普朗克值$0.315$），并比较固定背景推断与联合$(H_0,\,\Omega_m,\,\Xi)$推断。边缘化的$\Xi$后验为$0.9783 \pm 0.3548$，在此区间内无变化。联合推断给出$\Xi^{\rm joint} = 0.9550 \pm 0.3710$，$\Omega_m$与$\Xi$以及$H_0$与$\Xi$对的$|\rho| \lesssim 0.05$，而$\rho_{H_0 \Omega_m} \simeq -0.4$，$H_0$中位数在采用的$\Omega_m$范围内移动约$4.2\,{\rm km\,s^{-1}\,Mpc^{-1}}$。在固定$\Omega_m = 0.3$时对相同事件进行星系目录分析，$\Xi$的精度达到约$7.5\%$，而此处为$\pm 36.3\%$；较大的不确定性主要由宿主红移缺失导致。因此，即使暗警报主导检测率，亚百分比的$\Xi$测试仍将需要测量红移。
英文摘要
Binary black hole mergers without electromagnetic counterparts are expected to dominate O5 gravitational-wave catalogs. Recent CHIMERA~2.0 forecasts typically fix $Ω_m$ to a CMB-informed value and use spectroscopic hosts when available, but the corresponding sensitivity of the $Ξ$ posterior has not been assessed for pure dark sirens on the public O5 mock catalog. We analyze 300 O5-sensitivity mock events without galaxy catalogs, varying $Ω_m$ over $[0.20,\,0.35]$ (including Planck $0.315$), and compare fixed-background inference with joint $(H_0,\,Ω_m,\,Ξ)$ inference. The marginalized $Ξ$ posterior is $0.9783 \pm 0.3548$ and shows no change across this interval. Only GW luminosity distances enter the analysis, so the likelihood constrains $Ξ\, D_L^{\rm EM}(H_0,\,Ω_m)$; when $Ω_m$ is changed, $H_0$ shifts to compensate and the $Ξ$ marginal remains unchanged. Joint inference gives $Ξ^{\rm joint} = 0.9550 \pm 0.3710$, with $|ρ| \lesssim 0.05$ for the $Ω_m$--$Ξ$ and $H_0$--$Ξ$ pairs, whereas $ρ_{H_0 Ω_m} \simeq -0.4$ and the $H_0$ median moves by $\simeq 4.2\,{\rm km\,s^{-1}\,Mpc^{-1}}$ over the adopted $Ω_m$ range. Galaxy-catalog analyses on the same events at fixed $Ω_m = 0.3$ reach $\sim 7.5\%$ precision on $Ξ$, compared with $\pm 36.3\%$ here; the larger uncertainty is driven mainly by missing host redshifts. Sub-percent $Ξ$ tests will therefore still require measured redshifts even if dark sirens dominate the detection rate.
