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Gravitational wave (GW) signals from compact binary coalescences can be usedas standard sirens to constrain cosmological parameters if their redshift canbe measured independently. However, mergers of stellar binary black holes(BBHs) may not have electromagnetic counterparts and thus have no directredshift measurements. These dark sirens may be still used to statisticallyconstrain cosmological parameters by combining their GW measured luminositydistances and localization with deep redshift surveys of galaxies around it. Weinvestigate this dark siren method in detail by using mock BBH and galaxysamples. We find that the Hubble constant can be constrained well with anaccuracy $\lesssim1\%$ with a few tens or more of BBH mergers at redshift up to$1$ if GW observations can provide accurate estimates of their luminositydistance (with relative error of $\lesssim0.01$) and localization($\lesssim0.1~\rm{deg}^2$), though the constraint may be significantly biasedif the luminosity distance and localization errors are larger. We alsointroduce a simple method to correct this bias and find it is valid when theluminosity distance and localization errors are modestly large. We furthergenerate mock BBH samples, according to current constraints on BBH merger rateand the distributions of BBH properties, and find that the Deci-hertzObservatory (DO) in a half year observation period may detect about one hundredBBHs with signal-to-noise ratio $\varrho\gtrsim30$, relative luminositydistance error $\lesssim0.02$, and localization error $\lesssim0.01\rm{deg}^2$.By applying the dark standard siren method, we find that the Hubble constantcan be constrained to the $\sim0.1-1\%$ level using these DO BBHs, an accuracycomparable to the constraints obtained by using electromagnetic observations inthe near future, thus it may provide insight into the Hubble tension.

research in astronomy and astrophysics/research in astronomy and astrophysics

On Dark Gravitational Wave Standard Sirens as Cosmological Inference and  Forecasting the Constraint on Hubble Constant using Binary Black Holes  Detected by Deci-hertz Observatory