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

Abstract

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 $c_g\ne c$. We show that the case $c_g<c$ 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 $c-c_g<2\times 10^{-15}c$; if the cosmic rays have an extragalactic origin the bound is orders of magnitude tighter, of order $c-c_g<2\times 10^{-19}c$.

Comments: 8 pages with 1 figure, JHEP style. References added, slight (superficial) changes