Lorentz violation and higher-derivative gravity

TL;DR

This paper investigates a higher-derivative gravity model with Lorentz violation, analyzing its particle content, stability, and unitarity, and finds that Lorentz violation does not resolve the issues inherent in such models.

Contribution

The study introduces a new operator basis for analyzing Lorentz-violating higher-derivative gravity and assesses its implications for stability and unitarity.

Findings

Lorentz-violating term does not improve stability

Model remains non-unitary with higher derivatives

Operator basis aids in particle content analysis

Abstract

In this work, we analyze a gravity model with higher derivatives including a CPT-even Lorentz-violating term. In principle, the model could be a low-energy limit of a Lorentz-invariant theory presenting the violation of Lorentz symmetry as a consequence of a spontaneous symmetry-breaking mechanism if a decoupling between the metric and the Nambu-Goldstone modes is assumed. We have set up a convenient operator basis for the expansion of wave operators for symmetric second-rank tensors in the presence of a background vector. By using this set of operators, the particle content is obtained, and its consistency, regarding the conditions for stability and unitarity, is discussed. We conclude that this extra Lorentz noninvariant contribution is unable to address the problems of stability and unitarity of higher-derivative gravity models.