Effect of Deviations from General Relativity on Searches for Gravitational-wave Microlensing and Type II Strong Lensing

As the gravitational-wave (GW) detector network is upgraded and the sensitivity of the detectors improves, novel scientific avenues open for exploration. For example, tests of general relativity (GR) will become more accurate as smaller deviations can be probed. Additionally, the detection of lensed GWs becomes more likely. However, these new avenues could also interact with each other, and a GW event presenting deviations from GR could be mistaken for a lensed one. Here, we explore how phenomenological deviations from GR or binaries of exotic compact objects could impact those lensing searches focusing on a single event. We consider strong lensing, millilensing, and microlensing, and find that certain phenomenological deviations from GR may be mistaken for all of these types of lensing. Therefore, our study shows that future candidate lensing events would need to be carefully examined to avoid a false claim of lensing where instead a deviation from GR has been seen.