Constraining cosmological parameters from strong lensing with DECIGO and
  B-DECIGO sources
  Gravitational lensing has long been used to measure or constrain cosmology
models. Although the lensing effect of gravitational waves has not been
observed by LIGO/Virgo, it is expected that there can be a few to a few
hundreds lensed events to be detected by the future Japanese space-borne
interferometers DECIGO and B-DECIGO, if they are running for 4 years. Given the
predicted lensed gravitational wave events, one can estimate the constraints on
the cosmological parameters via the lensing statistics and the time delay
methods. With the lensing statistics method, the knowledge of the lens
redshifts, even with the moderate uncertainty, will set the tight bound on the
energy density parameter $\Omega_M$ for matter, that is,
$0.288\lesssim\Omega_M\lesssim0.314$ at best. The constraint on the Hubble
constant $H_0$ can be determined using the time delay method. It is found out
that at $5\sigma$, $|\delta H_0|/H_0$ ranges from $3\%$ to $11\%$ for DECIGO,
and B-DECIGO will give less constrained results, $8\%-15\%$. In this work, the
uncertainties on the luminosity distance and the time delay distance are set to
be $10\%$ and $20\%$, respectively. The improvement on measuring these
distances will tighten the bounds.
