Cosmology with a spin
  Using the chiral representation for spinors we present a particularly
transparent way to generate the most general spinor dynamics in a theory where
gravity is ruled by the Einstein-Cartan-Holst action. In such theories torsion
need not vanish, but it can be re-interpreted as a 4-fermion self-interaction
within a torsion-free theory. The self-interaction may or may not break parity
invariance, and may contribute positively or negatively to the energy density,
depending on the couplings considered. We then examine cosmological models
ruled by a spinorial field within this theory. We find that while there are
cases for which no significant cosmological novelties emerge, the
self-interaction can also turn a mass potential into an upside-down Mexican hat
potential. Then, as a general rule, the model leads to cosmologies with a
bounce, for which there is a maximal energy density, and where the cosmic
singularity has been removed. These solutions are stable, and range from the
very simple to the very complex.
