Stability in quadratic torsion theories

Abstract

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from the most general Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when torsion vanishes and investigating the behaviour of the vector and pseudovector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier.

A missing -1 factor in the pseudo-vectorial sector has been detected in Appendix D, conclusions partially changed in sections 3.3 and 4

References in corpus (4)

• f(R) Gravity with Torsion: The Metric-Affine Approach
• Constraining Torsion with Gravity Probe B
• f(R) cosmology with torsion
• Constraining spacetime torsion with the Moon and Mercury

Cited by in corpus (12)

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• Birkhoff's theorem for stable torsion theories
• Non-geodesic incompleteness in Poincaré gauge gravity
• Mimetic-Metric-Torsion with induced Axial mode and Phantom barrier crossing
• Cosmological Dark sector from a Mimetic-Metric-Torsion perspective
• Search for manifestations of spin-torsion coupling
• Axionic extension of the Proca action
• New effective theories of gravitation and their phenomenological consequences