Lorentz symmetry is relevant

TL;DR

This paper develops a covariant renormalisation group framework to study quantum fluctuations in Lorentz symmetry breaking theories of quantum gravity, revealing that small symmetry breakings are amplified at low energies, impacting observational constraints.

Contribution

The paper introduces a covariant renormalisation group equation on foliated spacetimes that preserves background diffeomorphism symmetry, applied to Lorentz symmetry breaking in quantum gravity.

Findings

Quantum fluctuations amplify Lorentz symmetry breaking at low energies.

Magnification of symmetry breaking is of order unity for compatible trajectories.

Observational constraints on Lorentz symmetry breaking are scale-independent.

Abstract

We set up a covariant renormalisation group equation on a foliated spacetime which preserves background diffeomorphism symmetry. As a first application of the new formalism, we study the effect of quantum fluctuations in Lorentz symmetry breaking theories of quantum gravity. It is found that once a small breaking is introduced e.g. at the Planck scale, quantum fluctuations enhance this breaking at low energies. A numerical analysis shows that the magnification is of order unity for trajectories compatible with a small cosmological constant. The immediate consequence is that the stringent observational constraints on Lorentz symmetry breaking are essentially scale-independent and must be met even at the Planck scale.