Effective matter dispersion relation in quantum covariant Horava-Lifshitz gravity

TL;DR

This paper investigates how quantum metric fluctuations in covariant Horava-Lifshitz gravity affect classical matter fields, revealing Lorentz-symmetry violations and constraining the theory's energy scale to align with experimental bounds.

Contribution

It provides a detailed analysis of matter dispersion relations in covariant Horava-Lifshitz gravity and establishes bounds on the theory's scale based on Lorentz violation constraints.

Findings

Quantum fluctuations induce Lorentz-symmetry violation in matter propagation.

The Horava-Lifshitz scale must be below 10^{10} GeV to satisfy current experimental bounds.

The model contains only logarithmic divergences due to classical matter fields.

Abstract

We study how quantum fluctuations of the metric in covariant Horava-Lifshitz gravity influence the propagation of classical fields (complex scalar and photon). The effective Lorentz-symmetry violation induced by the breaking of 4-dimensional diffeomorphism is then evaluated, by comparing the dressed dispersion relations for both external fields. The constraint of vanishing 3-dimensional Ricci scalar is imposed in the path integral, which therefore explicitly depends on two propagating gravitational degrees of freedom only. Because the matter fields are classical, the present model contains only logarithmic divergences. Furthermore, it imposes the characteristic Horava-Lifshitz scale to be smaller than $10^{10}$ GeV, if one wishes not to violate the current bounds on Lorentz symmetry violation.