Lower Bound on the Propagation Speed of Gravity from Gravitational Cherenkov Radiation

Recently, interesting 4-D Lorentz violating models have been proposed, in which all particles have a common maximum velocity c, but gravity propagates (in the preferred frame) with a different maximum velocity cg 6= c. We show that the case cg < c is very tightly constrained by the observation of the highest energy cosmic rays. Assuming a galactic origin for the cosmic rays gives a conservative bound of c− cg < 2× 10 c; if the cosmic rays have an extragalactic origin the bound is orders of magnitude tighter, of order c− cg < 2× 10 c.