Probing the Effects of Lorentz-Symmetry Violating Chern-Simons and Ricci-Cotton Terms in Higher Derivative Gravity

TL;DR

This paper explores how Lorentz-symmetry violating Chern-Simons and Ricci-Cotton terms affect higher derivative gravity, revealing that only the Einstein-Hilbert plus Chern-Simons term with a time-like vector remains free of tachyons and ghosts.

Contribution

It introduces a new operator basis simplifying propagator analysis and shows that spectral consistency requires turning off the Ricci-Cotton term in Lorentz-violating gravity.

Findings

The Einstein-Hilbert plus Chern-Simons model with a time-like vector is free of tachyons and ghosts.

Spectral consistency demands the Ricci-Cotton term be switched off.

Gravity with Lorentz-symmetry violation imposes unique constraints on background conditions.

Abstract

The combined effects of the Lorentz-symmetry violating Chern-Simons and Ricci-Cotton actions are investigated for the Einstein-Hilbert gravity in the second order formalism modified by higher derivative terms, and their consequences on the spectrum of excitations are analyzed. We follow the lines of previous works and build up an orthonormal basis of operators that splits the fundamental fields according to their individual degrees of freedom. With this new basis, the attainment of the propagators is remarkably simplified and the identification of the physical and unphysical modes gets a new insight. Our conclusion is that the only tachyon- and ghost-free model is the Einstein-Hilbert action added up by the Chern-Simons term with a time-like vector of the type $v^{\mu} = (\mu,\vec{0})$. Spectral consistency imposes taht the Ricci-Cotton term must be switched off. We then infer that gravity with Lorentz-symmetry violation imposes a drastically different constraint on the background if compared to usual gauge theories whenever conditions for suppression of tachyons and ghosts are required.