Probing the theory of gravity with gravitational lensing of gravitational waves and galaxy surveys

The cross-correlation of gravitational wave strain with upcoming galaxy surveys probes theories of gravity in a new way. This method enables testing the theory of gravity by combining the effects from both gravitational lensing of gravitational waves and the propagation of gravitational waves in space-time. We find that within 10 yr the combination of the Advanced LIGO (Laser Interferometer Gravitational-Wave Observatory) and VIRGO (Virgo interferometer) detector networks with planned galaxy surveys should detect weak gravitational lensing of gravitational waves in the low-redshift Universe (z < 0.5). With the next-generation gravitational wave experiments such as Voyager, LISA (Laser Interferometer Space Antenna), Cosmic Explorer, and the Einstein Telescope, we can extend this test of the theory of gravity to larger redshifts by exploiting the synergies between electromagnetic wave and gravitational wave probes.