Testing supermassive primordial black holes with lensing signals of binary black hole merges

Next-generation ground-based gravitational wave (GW) detectors are expected to observe millions of binary black hole mergers, a fraction of which will be strongly lensed by intervening galaxies or clusters, producing multiple images with characteristic distribution of time delay. Importantly, the predicted rate and properties of such events are sensitive to the abundance and distribution of strong lensing objects which directly depends on cosmological models. One such scenario posits the existence of supermassive primordial black holes (SMPBHs) in the early universe, which would enhance the formation of dark matter halos. This mechanism has been proposed to explain the abundance of high-redshift galaxies observed by James Webb Space Telescope. Crucially, the same cosmological model with SMPBHs would also leave a distinct imprint on the population of strongly lensed GWs. It predicts both an increased event rate and a modified distribution of time delays between the multiple images. Therefore, we propose statistical measurements of the rate and time delay distribution of strong lensing GW events as a powerful probe to directly constrain the abundance of SMPBHs. Considering $\Lambda$CDM cosmology with (non-)clustered SMPBHs, we find that the abundance of SMPBHs $f_{\rm PBH}$ with masses above $10^8~M_{\odot}$ is constrained to be $\sim10^{-4}$ at $95\%$ confidence level. It will be comparable and complementary to the currently available constraint from large scale structure observations.