Lensing of Gravitational Waves as a Novel Probe of Graviton Mass

Abstract: The diffraction patterns of lensed gravitational waves encode information about their propagation speeds. If gravitons have mass, the dispersion relation and speed of gravitational waves will be affected in a frequency-dependent manner, which would leave traces in the diffraction pattern if the waves are lensed. In this paper, we study how the alternative dispersion relation induced by massive gravitons affects gravitational waves lensed by point-mass lenses, such as intermediate-mass black holes. We find that the waveform morphology of lensed dispersive gravitational waves depends on the graviton mass more sensitively than their unlensed counterpart. Together with lensing amplification, the waveform-morphology modifications due to lensing can improve the measurement accuracy of the graviton mass. A single lensed gravitational-wave signal enables us to measure the graviton mass with an accuracy comparable with the combined measurement across $\mathcal{O}(10^3)$ unlensed signals. Our method allows us to incorporate lensed gravitational-wave signals into existing graviton-mass measurements. Our method can also be generalized to other lens types, gravitational-wave sources, and detector networks, preparing ourselves for thoroughly understanding the nature of gravitational waves in the era of lensed gravitational-wave astronomy.