Probability of gravitational-wave lensing by intermediate-mass black holes and globular clusters

Strongly lensed gravitational waves (GWs) are powerful probes of substructure in the lens. Intermediate-mass black holes (IMBHs) are postulated to be efficient lenses that may distort the lensed waveforms of currently detectable stellar-mass compact binaries, as hinted by GW231123. Assuming that IMBHs are located in globular clusters (GCs), we compute the rate at which they would affect strongly lensed repeated chirps produced by galaxy-scale lenses, considering a compound lens system. Exploring different astrophysical model assumptions and lensing criteria, we find that the relative rate is at most 1/1000 and decays to 1/10,000 for our fiducial optimistic scenario. At high magnifications, mu > 100, the relative rate approaches 1%, but these cases are intrinsically rare in absolute value. Our results imply that GW lensing by IMBHs and GCs is unlikely, disfavoring such an interpretation for GW231123. In turn, they point towards lensed GWs being a clean probe of dark matter substructures and primordial black holes.