Gravitational Wave Propagation for The Generalized Proca Theories

In general relativity, a gravitational wave propagates with the speed of light, but inthe alternative theories of gravity, propagation speed could deviate from the speed of lightdue to the modification of gravity. Gravitational waves are influenced by modified gravityduring propagation at the cosmological distance. In this paper, we investigate thepropagation of a gravitational wave of the generalized Proca theories by consideringgravitational wave as the gravitational field propagates in spacetime as a wave perturbing flatspacetime. We show that the arbitrary functions G3, G4, and G5 can be the sources ofdeviation of the speed of the gravitational wave.