Consistent Lorentz Violation in Flat and Curved Space

TL;DR

This paper explores frameworks where Lorentz violation occurs without altering spacetime geometry, identifying two classes of spontaneous Lorentz breaking that preserve Minkowski space even with gravity.

Contribution

It introduces two distinct classes of spontaneous Lorentz violation that do not affect the spacetime geometry, expanding understanding of Lorentz violation in gravitational contexts.

Findings

Two classes of Lorentz violation preserving Minkowski space identified

Tensor field condensation linked to ghost-condensation

Spontaneous Lorentz breaking in DGP and massive graviton models analyzed

Abstract

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 DGP 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.