2021MNRAS.507..761H

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 hundred 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 uncertainties, will set the tight bound on the energy density parameter Ω_M for matter, that is, 0.288 <= Ω_M <= 0.314 at best. The constraint on the Hubble constant H₀ can be determined using the time delay method. It is found out that at 5σ, |δH₀|/H₀ ranges from 3 per cent to 11 per cent for DECIGO, and B-DECIGO will give less constrained results, 8 per cent to 15 per cent. In this work, the uncertainties on the luminosity distance and the time delay distance are set to be 10 per cent and 20 per cent, respectively. The improvement on measuring these distances will tighten the bounds.