Eur. Phys. J. C (2020) 80: 611
https://doi.org/10.1140/epjc/s10052-020-8163-8

Regular Article - Theoretical Physics

Revisiting the stability of quadratic Poincaré gauge gravity

¹ Departamento de Física Fundamental and IUFFyM, Universidad de Salamanca, 37008, Salamanca, Spain
² Cosmology and Gravity Group, Department of Mathematics and Applied Mathematics, University of Cape Town, Rondebosch, Cape Town, 7701, South Africa
³ Van Swinderen Institute, University of Groningen, 9747 AG, Groningen, The Netherlands

^* e-mail: f.j.maldonado.torralba@rug.nl

Received: 6 May 2020
Accepted: 15 June 2020
Published online: 8 July 2020

Abstract

Poincaré gauge theories provide an approach to gravity based on the gauging of the Poincaré 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.