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 probe 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 spacetime. We find that within 10 years, the combination of the Advanced-LIGO and VIRGO detector networks with planned galaxy surveys should detect weak gravitational lensing of gravitational waves in the low redshift Universe ($z
16 pages, 7 figures. Minor changes in the text and added new references. Matches the version accepted for publication in MNRAS