Renormalizability of the Dirac equation in torsion gravity with nonminimal coupling

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