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