Gravitational waves at their own gravitational speed

Gravitational waves propagate at the speed of light in general relativity, because of its special relativistic basis. However, light propagation is linked to the electromagnetic phenomena, with the permittivity and permeability constants as the determining factors. Is there a deeper reason why waves in a geometric theory of gravity propagate at a speed determined by electromagnetic constants? What is the relation between gravity's own constants and the speed of gravitational waves? Our attempt to answer these fundamental questions takes us far and deep into the universe.