Revisiting the stability of quadratic Poincaré gauge gravity

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.

Generalized Birkhoff theorem in the Poincaré gauge gravity theory

“…The analysis of the validity of the generalized Birkhoff theorem helps to reduce the large number of the coupling constants in the general quadratic Lagrangian (1) to a set that determines a class of physically viable models which are consistent with Einstein's GR at large distances. Other criteria such as the unitarity and stability (absence of ghost and tachyon modes in the particle spectrum) impose additional restrictions on the coupling constants [46,47,53,[79][80][81][82][83][84][85][86][87][88], which should be combined with our findings.…”

Ghost-free higher-order theories of gravity with torsion

“…given that the conditions in (D.7) meet. The fact that the terms of the form ∇ μ K μ νρ ∇ σ K σ νρ are part of the Lagrangian has been proven recently to be a sufficient condition to make the vector modes present in the theory ghost-free in the IR limit [48].…”

“…We have shown that in Einstein equations the torsion vectors decouple from the metric under the stability conditions, hence obtaining the same metric solutions as in the case of a torsion-free IDG, see Eqs. (48) and (49), that are non-singular and free of ghosts. Nevertheless, since the axial part of the torsion is different from zero, the phenomenology of the solution would be different to the one in the null torsion case [34], despite sharing the same metric solution.…”

Nonlinearly ghost-free higher curvature gravity

“…Although one can find a ghost-free PGT at the level of linear perturbations about the flat background, the non-linear interactions may drastically change the structure of the theory. According to [27,28], it seems that the non-linearly ghostfree PGT can only contain the spin-0 modes in addition to the massless graviton (see also [29]). However, there is a non-linearly ghost-free PGT involving a massive spin-2 mode when an infinite number of appropriate higher curvature terms are added.…”