Maxwell’s field coupled nonminimally to quadratic torsion: Axion and birefringence

We consider a possible (parity conserving) interaction between the electromagnetic field F and a torsion field $T^{\alpha }$ of spacetime. For generic elementary torsion, gauge invariant coupling terms of lowest order fall into two classes that are both nonminimal and quadratic in torsion and respect Maxwell’s equations. The first class $\sim {\mathrm{FT}}^2$ admits $F$’s without the presence of charges and is excluded. The second class $\sim F^2{T}^2$ modifies the constitutive tensor of spacetime and can also be completely described in the framework of metricfree electrodynamics. We recognize three physical effects of the torsion: (i) An axion field that induces an optical activity into spacetime, (ii) a modification of the light cone structure that yields birefringence, and (iii) a torsion dependence of the velocity of light. We study these effects in the background of a Friedmann universe with torsion.