O5 dark-siren forecasts for modified GW propagation: background robustness of the $\hat{I}ž$ posterior

Abstract

Binary black hole mergers without electromagnetic counterparts are expected to dominate O5 gravitational-wave catalogs. Recent CHIMERA~2.0 forecasts typically fix $\hat{I}{\text{c◯}}_m$ to a CMB-informed value and use spectroscopic hosts when available, but the corresponding sensitivity of the $\hat{I}ž$ 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 $\hat{I}{\text{c◯}}_m$ over $[0.20,0.35]$ (including Planck $0.315$), and compare fixed-background inference with joint $(H_0,\hat{I}{\text{c◯}}_m,\hat{I}ž)$ inference. The marginalized $\hat{I}ž$ 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 $\hat{I}žD_L^{\mathrm{EM}}(H_0,\hat{I}{\text{c◯}}_m)$; when $\hat{I}{\text{c◯}}_m$ is changed, $H_0$ shifts to compensate and the $\hat{I}ž$ marginal remains unchanged. Joint inference gives $\hat{I}{ž}^{\mathrm{joint}}=0.9550\pm 0.3710$, with $|\ddot{I}|\lesssim 0.05$ for the $\hat{I}{\text{c◯}}_m$--$\hat{I}ž$ and $H_0$--$\hat{I}ž$ pairs, whereas $\ddot{I}{}_{H_0\hat{I}{\text{c◯}}_m}\simeq -0.4$ and the $H_0$ median moves by $\simeq 4.2\mathrm{km}{\mathrm{s}}^{-1}\mathrm{Mp}{\mathrm{c}}^{-1}$ over the adopted $\hat{I}{\text{c◯}}_m$ range. Galaxy-catalog analyses on the same events at fixed $\hat{I}{\text{c◯}}_m=0.3$ reach $\sim 7.5\%$ precision on $\hat{I}ž$, compared with $\pm 36.3\%$ here; the larger uncertainty is driven mainly by missing host redshifts. Sub-percent $\hat{I}ž$ tests will therefore still require measured redshifts even if dark sirens dominate the detection rate.

10 pages, 4 figures

Topics & keywords