Vector models of gravitational Lorentz symmetry breaking

Abstract

Spontaneous Lorentz symmetry breaking can occur when the dynamics of a tensor field cause it to take on a nonzero expectation value in vacuo, thereby providing one or more ``preferred directions'' in spacetime. Couplings between such fields and spacetime curvature will then affect the dynamics of the metric, leading to interesting gravitational effects. Bailey and Kosteleck\'y [Q. G. Bailey and V. A. Kosteleck\'y, Phys. Rev. D 74, 045001 (2006)] developed a post-Newtonian formalism that, under certain conditions concerning the field's couplings and stress-energy, allows for the analysis of gravitational effects in the presence of Lorentz symmetry breaking. We perform a systematic survey of vector models of spontaneous Lorentz symmetry breaking. We find that a two-parameter class of vector models, those with kinetic terms we call ``pseudo-Maxwell,'' can be successfully analyzed under the Bailey-Kosteleck\'y formalism, and that one of these two ``dimensions'' in parameter space has not yet been explored as a possible mechanism of spontaneous Lorentz symmetry breaking.