Spontaneous Lorentz breaking at high energies

Theories that spontaneously break Lorentz invariance also violatediffeomorphism symmetries, implying the existence of extra degrees of freedomand modifications of gravity. In the minimal model (``ghost condensation'')with only a single extra degree of freedom at low energies, the scale ofLorentz violation cannot be larger than about M ~ 100GeV due to an infraredinstability in the gravity sector. We show that Lorentz symmetry can be brokenat much higher scales in a non-minimal theory with additional degrees offreedom, in particular if Lorentz symmetry is broken by the vacuum expectationvalue of a vector field. This theory can be constructed by gauging ghostcondensation, giving a systematic effective field theory description thatallows us to estimate the size of all physical effects. We show that nonlineareffects become important for gravitational fields with strength \sqrt{\Phi} >g, where g is the gauge coupling, and we argue that the nonlinear dynamics isfree from singularities. We then analyze the phenomenology of the model,including nonlinear dynamics and velocity-dependent effects. The strongestbounds on the gravitational sector come from either black hole accretion ordirection-dependent gravitational forces, and imply that the scale ofspontaneous Lorentz breaking is M < Min(10^{12}GeV, g^2 10^{15}GeV). If theLorentz breaking sector couples directly to matter, there is a spin-dependentinverse-square law force, which has a different angular dependence from theforce mediated by the ghost condensate, providing a distinctive signature forthis class of models.Comment: 60 pages, 6 figures; version accepted for publication in JHE