Einstein-aether as a quantum effective field theory

TL;DR

This paper analyzes the Einstein-aether theory as a quantum effective field theory, demonstrating its controlled expansion, absence of log-running for key parameters, and estimating matter Lorentz-violation effects to refine experimental bounds.

Contribution

It provides a detailed quantum effective field theory analysis of Einstein-aether, establishing its renormalization properties and deriving new bounds on Lorentz-violating parameters.

Findings

Controlled effective expansion within dimensional regularisation.

No log-running of two-derivative phenomenological parameters.

Estimated matter Lorentz-violation effects and derived new bounds.

Abstract

The possibility that Lorentz symmetry is violated in gravitational processes is relatively unconstrained by experiment, in stark contrast with the level of accuracy to which Lorentz symmetry has been confirmed in the matter sector. One model of Lorentz violation in the gravitational sector is Einstein-aether theory, in which Lorentz symmetry is broken by giving a vacuum expectation value to a dynamical vector field. In this paper we analyse the effective theory for quantised gravitational and aether perturbations. We show that this theory possesses a controlled effective expansion within dimensional regularisation, that is, for any process there are a finite number of Feynman diagrams which will contribute to a given order of accuracy. We find that there is no log-running of the two-derivative phenomenological parameters, justifying the use of experimental constraints for these parameters obtained over many orders of magnitude in energy scale. Given the stringent experimental bounds on two-derivative Lorentz-violating operators, we estimate the size of matter Lorentz-violation which arises due to loop effects. This amounts to an estimation of the natural size of coefficients for Lorentz-violating dimension-six matter operators, which in turn can be used to obtain a new bound on the two-derivative parameters of this theory.