Lorentz Violation in Goldstone Gravity

TL;DR

This paper explores a gravity theory with spontaneous Lorentz violation via a tensor vev, leading to Goldstone modes resembling gravitons, and investigates their modified dispersion relations and observational constraints.

Contribution

It introduces a model where Lorentz symmetry is spontaneously broken in gravity, resulting in Goldstone gravitons with unique properties and potential observable effects.

Findings

Goldstone modes mimic gravitons in certain conditions

Lorentz-violating corrections modify graviton dispersion relations

Cosmic ray observations can constrain Lorentz-violating effects

Abstract

We consider a theory of gravity in which a symmetric two-index tensor in Minkowski spacetime acquires a vacuum expectation value (vev) via a potential, thereby breaking Lorentz invariance spontaneously. When the vev breaks all the generators of the Lorentz group, six Goldstone modes emerge, two linear combinations of which have properties that are identical to those of the graviton in general relativity. Integrating out massive modes yields an infinite number of Lorentz-violating radiative-correction terms in the low-energy effective Lagrangian. We examine a representative subset of these terms and show that they modify the dispersion relation of the two propagating graviton modes such that their phase velocity is direction-dependent. If the phase velocity of the Goldstone gravitons is subluminal, cosmic rays can emit gravi-Cherenkov radiation, and the detection of high-energy cosmic rays can be used to constrain these radiative correction terms. Test particles in the vicinity of the Goldstone gravitons undergo longitudinal oscillations in addition to the usual transverse oscillations as predicted by general relativity. Finally, we discuss the possibility of having vevs that do not break all six generators and examine in detail one such theory.