Lorentz-violating vs ghost gravitons: the example of Weyl gravity

TL;DR

This paper explores how breaking local Lorentz symmetry can eliminate ghost degrees of freedom in Einstein gravity with a Weyl term, affecting the behavior of primordial gravitational waves in cosmology.

Contribution

It introduces a simple mechanism to remove ghost modes via Lorentz symmetry breaking and analyzes its effects on tensor perturbations in a cosmological context.

Findings

Ghosts can be eliminated by Lorentz symmetry breaking.

The tensor spectrum amplitude diverges near the Lorentz-violating scale.

Contrasts with standard Weyl gravity where ghosts damp primordial waves.

Abstract

We show that the ghost degrees of freedom of Einstein gravity with a Weyl term can be eliminated by a simple mechanism that invokes local Lorentz symmetry breaking. We demonstrate how the mechanism works in a cosmological setting. The presence of the Weyl term forces a redefinition of the quantum vacuum state of the tensor perturbations. As a consequence the amplitude of their spectrum blows up when the Lorentz-violating scale becomes comparable to the Hubble radius. Such a behaviour is in sharp contrast to what happens in standard Weyl gravity where the gravitational ghosts smoothly damp out the spectrum of primordial gravitational waves.