Gravitational Waves in Doubly Coupled Bigravity

We consider gravitational waves from the point of view of both their production and their propagation in doubly coupled bigravity in the metric formalism. In bigravity, the two gravitons are coupled by a non-diagonal mass matrix and show birefrigence. In particular, we find that one of the two gravitons propagates with a speed which differs from one. This deviation is tightly constrained by both the gravitational Cerenkov effect and the energy loss of binary pulsars. When emitted from astrophysical sources, the Jordan frame gravitational wave, which is a linear combination of the two propagating gravitons, has a wave form displaying beats. The best prospect of detecting this phenomenon would come from nano-Hertz interferometric experiments.