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

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.

20 pages, 0 figures

References in corpus (5)

• Cuscuton: A Causal Field Theory with an Infinite Speed of Sound
• Cuscuton Cosmology: Dark Energy meets Modified Gravity
• Addressing $H_0$ tension with emergent dark radiation in unitary gravity
• Mapping Poincaré gauge cosmology to Horndeski theory for emergent dark energy
• Adiabatic Solutions in General Relativity and Boundary Symmetries

Cited by in corpus (5)

• Note on the absence of the second clock effect in Weyl gauge theories of gravity
• Supercomputers against strong coupling in gravity with curvature and torsion
• Einstein-Proca theory from the Einstein-Cartan formulation
• Hamiltonian formulation of gravity as a spontaneously-broken gauge theory of the Lorentz group
• Geometric multipliers and partial teleparallelism in Poincaré gauge theory