Constraint on modified dispersion relations for gravitational waves from gravitational Cherenkov radiation

Abstract

We investigate the hypothetical process of gravitational Cherenkov radiation, which may occur in modified gravity theories. We obtain a useful constraint on a modified dispersion relation for propagating modes of gravitational waves, which could be predicted as a consequence of violation of the Lorentz invariance in modified theories of gravity. The constraint from gravitational Cherenkov radiation and that from direct measurements of the gravitational waves emitted by a compact binary system are complementary to each other.