Revisiting the Stability of Quadratic Poincar\'e Gauge Gravity

TL;DR

This paper investigates the stability of quadratic Poincaré gauge gravity theories, revealing ghost issues in the axial sector and exploring special parameter choices that yield dynamical scalars, linking to Brans-Dicke and Holst theories.

Contribution

The study provides a detailed ghost analysis of quadratic Poincaré gauge theories and identifies conditions for ghost-free models with dynamical torsion scalars.

Findings

Axial sector exhibits ghostly couplings leading to instability.

Imposing ghost-freedom often results in non-dynamical torsion.

Special parameter choices yield dynamical scalar fields related to known theories.

Abstract

Poincar\'e gauge theories provide an approach to gravity based on the gauging of the Poincar\'e group, whose homogeneous part generates curvature while the translational sector gives rise to torsion. In this note we revisit the stability of the widely studied quadratic theories within this framework. We analyse the presence of ghosts without fixing any background by obtaining the relevant interactions in an exact post-Riemannian expansion. We find that the axial sector of the theory exhibits ghostly couplings to the graviton sector that render the theory unstable. Remarkably, imposing the absence of these pathological couplings results in a theory where either the axial sector or the torsion trace becomes a ghost. We conclude that imposing ghost-freedom generically leads to a non-dynamical torsion. We analyse however two special choices of parameters that allow a dynamical scalar in the torsion and obtain the corresponding effective action where the dynamics of the scalar is apparent. These special cases are shown to be equivalent to a generalised Brans-Dicke theory and a Holst Lagrangian with a dynamical Barbero-Immirzi pseudoscalar field respectively. The two sectors can co-exist giving a bi-scalar theory. Finally, we discuss how the ghost nature of the vector sector can be avoided by including additional dimension four operators.