Renormalizability of the Dirac Equation in Torsion-Gravity with Non-Minimal Coupling

TL;DR

This paper demonstrates that non-minimal fermionic couplings in torsion-gravity theories can be renormalized and may prevent cosmological singularities, challenging the usual neglect of such couplings due to ultraviolet issues.

Contribution

It shows that including torsion allows non-minimal couplings to be well-behaved and renormalizable, with implications for parity violation and singularity avoidance in cosmology.

Findings

Non-minimal couplings can be renormalized with torsion.

Torsion can prevent cosmological singularities.

Parity-odd effects may arise in the gravitational sector.

Abstract

We will consider the torsional completion of gravity for a background filled with Dirac matter fields, studying what happens when fermionic non-minimal coupling is taken into account: we will show that, although non-minimal couplings are usually disregarded because of their ill-defined behaviour in ultraviolet regimes, this is due to the fact that torsion is commonly neglected, whereas when torsion is not left aside, even non-minimal couplings behave properly. In detail, we will see that non-minimal coupling allows to renormalize the Dirac equation even when torsion is taken into consideration and that in some type of non-minimally coupled models parity-oddness might be present even in the gravitational sector. In addition, we will show that in the presence of the considered non-minimal coupling, torsion is able to evade cosmological singularities as it can happen in the minimal coupling case and in some other non--minimally coupled theory. In the course of the paper, we shall consider a specific interaction as prototype to study this fermionic non-minimal coupling, but we will try to present results that do not depend on the actual structure of the non-minimal couplings by investigating alternative types of interaction.