Gravity with a dynamical preferred frame - art. no. 024028

We study a generally covariant model in which local Lorentz invariance is b roken by a dynamical unit timelike vector field u(a)-the "aether." Such a m odel makes it possible to study the gravitational and cosmological conseque nces of preferred frame effects, such as "variable speed of light" or high frequency dispersion, while preserving a generally covariant metric theory of gravity. In this paper we restrict attention to an action for an effecti ve theory of the aether which involves only the antisymmetrized derivative del ([a)u(b]). Without matter this theory is equivalent to a sector of the Einstein-Maxwell-charged dust system. The aether has two massless transvers e excitations, and the solutions of the model include all vacuum solutions of general relativity (as well as other solutions). However, the aether gen erally develops gradient singularities which signal a breakdown of this eff ective theory. Including the symmetrized derivative in the action for the a ether field may cure this problem.