Spin connection as Lorentz gauge field: propagating torsion

TL;DR

This paper introduces a modified gravitational action with quadratic Lorentz gauge terms, leading to propagating torsion with distinct degrees of freedom, including a pseudo-scalar and a tachyon, affecting matter interactions.

Contribution

It presents a novel gravitational model incorporating quadratic Lorentz gauge terms that results in propagating torsion with unique particle-like excitations.

Findings

Identifies six torsion degrees of freedom: one pseudo-scalar and five tachyons.

Shows pseudo-scalar couples to fermions with suppressed coupling constant.

Demonstrates tachyon causes causality violation via gravitational interactions.

Abstract

We propose a modified gravitational action containing besides the Einstein-Cartan term some quadratic contributions resembling the Yang-Mills lagrangian for the Lorentz spin connections. We outline how a propagating torsion arises and we solve explicitly the linearised equations of motion on a Minkowski background. We identify among torsion components six degrees of freedom: one is carried by a pseudo-scalar particle, five by a tachyon field. By adding spinor fields and neglecting backreaction on the geometry, we point out how only the pseudo-scalar particle couples directly with fermions, but the resulting coupling constant is suppressed by the ratio between fermion and Planck masses. Including backreaction, we demonstrate how the tachyon field provides causality violation in the matter sector, via an interaction mediated by gravitational waves.