Inferring the lensing rate of LIGO-Virgo sources from the stochastic gravitational wave background

Strong lensing of gravitational waves (GWs) is more likely for distant sources but predicted event rates are highly uncertain with many astrophysical origins proposed. Here, we open a new avenue to estimate the event rate of strongly lensed systems by exploring the amplitude of the stochastic gravitational wave background (SGWB). This method can provide a direct upper bound on the high-redshift binary coalescing rates, which can be translated into an upper bound on the expected rate of strongly lensed systems. We show that from the ongoing analysis of the Laser Interferometer Gravitational-wave Observatory (LIGO)-Virgo and in the future from the LIGO-Virgo design sensitivity stringent bounds on the lensing event rate can be imposed using the SGWB signal. Combining measurements of loud GW events with an unresolved stochastic background detection will improve estimates of the numbers of lensed events at high redshift. The proposed method is going to play a crucial in understanding the population of lensed and unlensed systems from GW observations.