### Spin connection as Lorentz gauge field: propagating torsion

(0 votes over all institutions)

We propose a modified gravitational action containing besides the Einstein-Hilbert term some quadratic contributions resembling the Yang-Mills lagrangian for the 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, we point out how only the pseudo-scalar particle couples directly with fermions and we evaluate the associated coupling constant, which is suppressed by the ratio between fermion and Planck masses.