Nonlinear Hamiltonian analysis of new quadratic torsion theories Part I. Cases with curvature-free constraints

TL;DR

This paper analyzes the nonlinear Hamiltonian structure of specific quadratic torsion gravity theories, confirming their linear properties but revealing potential issues like broken gauge symmetry and non-viable cosmological backgrounds.

Contribution

It investigates the nonlinear dynamics of eight quadratic torsion theories with curvature-free constraints, highlighting qualitative changes and limitations in their physical viability.

Findings

All eight theories are unitary and ghost-free at linear level.

Nonlinear regimes show broken gauge symmetry and possible acausal behavior.

Two theories' massless modes are vector excitations, not gravitons.

Abstract

It was recently found that, when linearised in the absence of matter, 58 cases of the general gravitational theory with quadratic curvature and torsion are (i) free from ghosts and tachyons and (ii) power-counting renormalisable. We inspect the nonlinear Hamiltonian structure of the eight cases whose primary constraints do not depend on the curvature tensor. We confirm the particle spectra and unitarity of all these theories in the linear regime. We uncover qualitative dynamical changes in the nonlinear regimes of all eight cases, suggesting at least a broken gauge symmetry, and possibly the activation of negative kinetic energy spin-parity sectors and acausal behaviour. Two of the cases propagate a pair of massless modes at the linear level, and were interesting as candidate theories of gravity. However, we identify these modes with vector excitations, rather than the tensor polarisations of the graviton. Moreover, we show that these theories do not support a viable cosmological background.