Spontaneous Lorentz Breaking at High Energies

TL;DR

This paper explores how Lorentz symmetry can be spontaneously broken at high energies through non-minimal models involving vector fields, leading to observable effects and constraints from astrophysical phenomena.

Contribution

It introduces a gauged ghost condensation framework allowing high-scale Lorentz breaking with systematic effective field theory analysis.

Findings

Lorentz violation scale can reach up to 10^{12} GeV or higher.

Nonlinear gravitational effects are significant for strong fields but remain well-behaved.

Distinctive spin-dependent inverse-square law forces could serve as experimental signatures.

Abstract

Theories that spontaneously break Lorentz invariance also violate diffeomorphism symmetries, implying the existence of extra degrees of freedom and modifications of gravity. In the minimal model (``ghost condensation'') with only a single extra degree of freedom at low energies, the scale of Lorentz violation cannot be larger than about M ~ 100GeV due to an infrared instability in the gravity sector. We show that Lorentz symmetry can be broken at much higher scales in a non-minimal theory with additional degrees of freedom, in particular if Lorentz symmetry is broken by the vacuum expectation value of a vector field. This theory can be constructed by gauging ghost condensation, giving a systematic effective field theory description that allows us to estimate the size of all physical effects. We show that nonlinear effects become important for gravitational fields with strength \sqrt{\Phi} > g, where g is the gauge coupling, and we argue that the nonlinear dynamics is free from singularities. We then analyze the phenomenology of the model, including nonlinear dynamics and velocity-dependent effects. The strongest bounds on the gravitational sector come from either black hole accretion or direction-dependent gravitational forces, and imply that the scale of spontaneous Lorentz breaking is M < Min(10^{12}GeV, g^2 10^{15}GeV). If the Lorentz breaking sector couples directly to matter, there is a spin-dependent inverse-square law force, which has a different angular dependence from the force mediated by the ghost condensate, providing a distinctive signature for this class of models.