  Gravitational waves (GWs) originated from mergers of stellar-mass binary
black holes (SBBHs) are considered as dark sirens in cosmology since they
usually do not have electromagnetic counterparts. In order to study cosmos with
these events, we not only need the luminosity distances extracted from GW
signals, but also require the redshift information of sources via, say,
matching GW sky localization with galaxy catalogs. Based on such a methodology,
we explore how well decihertz GW detectors, DO-Optimal and DECIGO, can
constrain cosmological parameters. Using Monte-Carlo simulated dark sirens, we
find that DO-Optimal can constrain the Hubble parameter to ${\sigma_{H_0}} /
{H_0}\, \lesssim 0.23\%$ when estimating $H_0$ alone, while DECIGO performs
better by a factor of 5 with ${\sigma_{H_0}} / {H_0}\lesssim 0.043\%$. Such a
good precision of $H_0$ will shed light on the $H_0$ tension. For
multiple-parameter estimation, DECIGO can still reach a level of relative
uncertainty smaller than $7\%$. The reason why decihertz detectors perform well
is explained by their large numbers of SBBH GW events with good distance and
angular resolution.
