Constraining the New Aether: gravitational Cherenkov radiation

We study the simplest concrete theory for spontaneous Lorentz violation, the New Aether theory of Jacobson and Mattingly, which is a vector-tensor gravitational theory with a fixed-modulus condition on the vector field. We show that the observation of ultra-high energy cosmic rays ( which implies the absence of energy loss via various Cherenkov type processes) places constraints on the parameters of this theory, which are much stronger than those previously found in the literature and are also stronger than the constraints generically arising when gravity displays sub-luminal propagation.