Model-Independent Search Discards Faint Lensed-Pairs of Gravitational Wave Events in the Sub-Threshold Candidates of GWTC-4
Gravitational lensing of gravitational waves (GWs) can produce multiple images in the geometric optics limit. These lensed GW images arrive at different times, are amplified by different magnification factors, and are shifted by constant phases. With current understanding, the occurrence of lensed events stands at a few per thousand events, and the number of GW detections is a few hundred with the ground-based detector network. However, with the inclusion of the sub-threshold events, the total number of detections crosses a few thousand. Therefore, a search that includes both types of events yields a higher chance of lensing detection. In this work, we carry out the first model-independent lensing search using a cross-correlation-based technique GLANCE over the entire volume of the GWTC-4 strain data, containing $\sim 90$ super-events $\sim 800$ sub-events forming a total of $\sim 11,000$ event pairs with a higher False Alarm Rate (FAR) event rate allowing to search deep in the noise dominated regime. We further conduct their spectrogram checks to inspect data quality, sky-map overlap of the interesting pairs, and a Bayesian parameter exploration of the sub-event to make a robust lensing detection. Although the search indicated four pairs of potential events with cross-correlation significance $\geq 2σ$, none were above $3σ$ at both the LIGO-Hanford and LIGO-Livingston detectors. This makes it possible to strongly rule out the presence of any statistically significant sub-threshold lensed GW event in GWTC-4. The null detection translates to an upper bound on the lensing detection rate to be $\leq$ 1.5/yr with inclusion of the sub-threshold event candidates. In the future, with more observation time, the detection of lensed GW can be possible from the current generation of GW detectors.