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The cross-correlation of gravitational wave strain with upcoming galaxysurveys probe theories of gravity in a new way. This method enables testing thetheory of gravity by combining the effects from both gravitational lensing ofgravitational waves and the propagation of gravitational waves in spacetime. Wefind that within 10 years, the combination of the Advanced-LIGO and VIRGOdetector networks with planned galaxy surveys should detect weak gravitationallensing of gravitational waves in the low redshift Universe ($z<0.5$). With thenext generation gravitational wave experiments such as Voyager, LISA,Cosmic-Explorer and Einstein Telescope, we can extend this test of the theoryof gravity to larger redshifts by exploiting the synergies betweenelectromagnetic wave and gravitational wave probes.

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