Search for gravitational-lensing signatures in the full third observing run of the LIGO–Virgo network

Gravitational lensing by massive objects in between the source and observer leads to distortions to gravitational-wave signals that may reveal additional information about fundamental physics, cosmology, and astrophysics. In this work, we have extended the search for lensing signatures to all black hole binary events from the third observing run of the LIGO--Virgo network. We search for repeated signals from strong lensing by 1) performing targeted searches for subthreshold signals, 2) calculating the degree of overlap between the intrinsic parameters and sky location, 3) comparing the similarities of the spectrograms, and 4) performing dual-signal Bayesian analysis that takes into account selection effects and astrophysical knowledge. We also search for distortions to the gravitational waveform caused by 1) frequency-independent phase shifts in strongly lensed images, and 2) frequency-dependent modulation of the amplitude and phase due to point masses. None of these searches yields significant evidence for lensing. Finally, we use the non-detection of gravitational-wave lensing to study the lensing rate based on the latest merger-rate estimates and set constraints on the dark matter fraction of (dark) compact objects.