A square-torsion modification of Einstein-Cartan theory



In the present paper a theory of gravity is considered in which not only curvature but also torsion is explicitly present in the Lagrangian, both with their own coupling constant. In particular, the couplings to Dirac fields and spin fluids are discussed: in the case of Dirac fields, it is discusses how the Dirac self-interactions depend on the coupling constant as a parameter that may even make these non-linearitiesmanifest at subatomic scales, showing different applications according to the value of the parameter assigned; in the case of spin fluids, FLRW cosmological models arising from the proposed theory are discussed.