Is the Graviton a Goldstone Boson?

A theory is outlined in which Lorentz invariance is spontaneously violated, giving rise to a constant vector field ${\lambda }^{\mu }$. The two quantities which are most simply related to ${\lambda }^{\mu }$ are the gravitational constant $\mathcal{G}$ and the decay rate of $K_2^{}{}_{}{}^0\to 2\pi$, assuming that the latter will eventually show an energy dependence. Using a method suggested by Bjorken for electrodynamics, we conclude that the model may support a graviton, and determine the order of magnitude of $\mathcal{G}$. A simple argument relates the $K_2^{}{}_{}{}^0$ decay to $\mathcal{G}$; the agreement with experiment is good.