  The purpose of this work is to investigate the prospects of using the future
standard siren data without redshift measurements to constrain cosmological
parameters. With successful detections of gravitational wave (GW) signals an
era of GW astronomy has begun. Unlike the electromagnetic domain, GW signals
allow direct measurements of luminosity distances to the sources, while their
redshifts remain to be measured by identifying electromagnetic counterparts.
This leads to significant technical problems for almost all possible BH-BH
systems. It is the major obstacle to cosmological applications of GW standard
sirens. In this paper, we introduce the general framework of using luminosity
distances alone for cosmological inference. The idea is to use the prior
knowledge of the redshift probability distribution for coalescing sources from
the intrinsic merger rates assessed with population synthesis codes. Then the
posterior probability distributions for cosmological parameters can be
calculated. We demonstrate the performance of our method on the simulated mock
data and show that the luminosity distance measurement would enable an accurate
determination of cosmological parameters up to $20%$ uncertainty level. We also
find that in order to infer $H_0$ to 1% level with flat $\Lambda$CDM model, we
need about $10^5$ events.
