Vector models of gravitational Lorentz symmetry breaking

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 Kostelecky [Q. G. Bailey and V. A. Kostelecky, 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-Kostelecky 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.