Revisiting the stability of quadratic Poincaré gauge gravity

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...

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Bibliographic Details
Published in:The European physical journal. C, Particles and fields Particles and fields, 2020-07, Vol.80 (7), p.1-16, Article 611
Main Authors: Jiménez, Jose Beltrán, Torralba, Francisco José Maldonado
Format: Article
Language:English
Subjects:
Astronomy
Astrophysics and Cosmology
Couplings
Elementary Particles
Gaging
Ghosts
Gravitation
Gravitons
Hadrons
Heavy Ions
Measurement Science and Instrumentation
Nuclear Energy
Nuclear Physics
Physics
Physics and Astronomy
Quantum Field Theories
Quantum Field Theory
Regular Article - Theoretical Physics
Stability analysis
String Theory
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Summary: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.
ISSN:1434-6044
1434-6052
DOI:10.1140/epjc/s10052-020-8163-8