The particle spectrum of parity-violating Poincar\'e gravitational theory

TL;DR

This paper analyzes the particle spectrum of a parity-violating Poincaré gravitational theory, identifying conditions for physical, ghost-free, and tachyon-free degrees of freedom, and showing how parity-odd terms expand the viable parameter space.

Contribution

It extends the analysis of Poincaré gravity by including parity-odd invariants and develops a formalism to handle these in the spectrum analysis.

Findings

Parity-odd invariants enlarge the healthy parameter space.

Conditions for ghost and tachyon freedom are derived.

The spin-projection operator formalism is extended for parity-odd analysis.

Abstract

In this paper we investigate the physical spectrum of the gravitational theory based on the Poincar\'e group with terms which are at most quadratic in tetrad and spin connection, allowing for the presence of parity-even as well as parity-odd invariants. We determine restrictions on the parameters of the action so that all degrees of freedom propagate and are neither ghosts nor tachyons. We show that the addition of parity non-conserving invariants extends the healthy parameter space of the theory. To accomplish our goal, we apply the weak field approximation around flat spacetime and in order to facilitate the analysis, we separate the bilinear action for the excitations into completely independent spin sectors. For this purpose, we employ the spin-projection operator formalism and extend the original basis built previously, to be able to handle the parity-odd pieces.