Gravitational Wave Oscillations in Bigravity

We derive consistent equations for gravitational wave oscillations in bigravity. In this framework a second dynamical tensor field is introduced in addition to general relativity and coupled such that one massless and one massive linear combination arise. Only one of the two tensors is the physical metric coupling to matter, and thus the basis in which gravitational waves propagate is different from the basis where the wave is produced and detected. Therefore, one should expect-in analogy to neutrino oscillations-to observe an oscillatory behavior. We show for the first time how this behavior arises explicitly, discuss phenomenological implications, and present new limits on the graviton parameter space in bigravity.