Consistent Lorentz violation in flat and curved space

Motivated by the severity of the bounds on Lorentz violation in the presence of ordinary gravity, we study frameworks in which Lorentz violation does not affect the spacetime geometry. We show that there are at least two inequivalent classes of spontaneous Lorentz breaking that even in the presence of gravity result in Minkowski space. The first one generically corresponds to the condensation of tensor fields with tachyonic mass, which in turn is related to ghost condensation. In the second class, realized by the Dvali-Gabadadze-Porrati model or theories of massive gravitons, spontaneous Lorentz breaking is induced by the expectation value of sources. The generalization to de Sitter space is also discussed.

Figure 1

Left: conformal diagrams of the solution with de Sitter branes. The bulk consists of Schwarzschild–de Sitter space with negative mass, which has two naked singularities, one at each pole. The static chart displayed in (b1) covers the interior of the left diamond. In order to avoid the singularity, we have to take $\rho <0$. Still, we have to avoid the other one, which can be accomplished by placing another brane with the same kind of fluid after the equator, represented with the dashed line. Right: conformal diagram for the solution with a flat brane supporting a fluid with generic equation of state. The bulk is Schwarzschild-AdS space with positive mass. The effective brane tension is negative, so the solution corresponds to the exterior, including the AdS boundary. The background solution does not depend on $M_4$, but gravity is not effectively four dimensional unless the DGP term is included.