Possible discrimination of black hole origins from the lensing rate of DECIGO and B-DECIGO sources

In this paper, we forecast the expected detection rates and redshift distributions of gravitationally lensed gravitational waves (GWs) from three different mass distributions of primordial black holes (PBHs) and two stellar formation models of astrophysical black holes (ABHs) in the context of DECi-hertz Interferometer Gravitational wave Observatory (DECIGO) and it's smaller scale version B-DECIGO. It suggests that DECIGO will be able to detect $10^4-10^5$ GW signals from such binary black holes (BBHs) each year and the event rate distributions for PBHs will differ from those for ABHs due to their different merger rate with respect to redshift. The large number of event rates make $5-100$ detections of lensed GW signals being possible. After considering the gravitational lensing effect, the difference between the detection rates and distributions for PBHs and ABHs will be more significant. Therefore, this can be served as a complementary method to distinguish PBHs from ABHs.