The propagation of classical gravitational waves in Bianchi type-I universes is studied. We find that gravitational waves in Bianchi type-I universes are not equivalent to two minimally coupled massless scalar fields as in the Robertson-Walker universe. Because of its tensorial nature, the gravitational wave is much more sensitve to the anisotropy of the spacetime than the scalar field is and it gains an effective mass term. Moreover, we find a coupling between the two polarization states of the gravitational wave which is also not present in the Robertson-Walker universe.
Physical Review D (Particles and Fields) 52(10), pp.5445-5458