  We consider a generalized Einstein-Cartan theory, in which we add the unique
covariant dimension four operators to general relativity that couples fermionic
spin current to the torsion tensor (with an arbitrary strength). Since torsion
is local and non-dynamical, when integrated out it yields an effective
four-fermion interaction of the gravitational strength. We show how to
renormalize the theory, in the one-loop perturbative expansion in generally
curved space-times, obtaining the first order correction to the 2PI effective
action in Schwinger-Keldysh (${\it in-in}$) formalism. We then apply the
renormalized theory to study the dynamics of a collapsing universe that begins
in a thermal state and find that -- instead of a big crunch singularity -- the
Universe with torsion undergoes a ${\it bounce}$. We solve the dynamical
equations (a) classically (without particle production); (b) including the
production of fermions in a fixed background in the Hartree-Fock approximation
and (c) including the quantum backreaction of fermions onto the background
space-time. In the first and last cases the Universe undergoes a bounce. The
production of fermions due to the coupling to a contracting homogeneous
background speeds up the bounce, implying that the quantum contributions from
fermions is negative, presumably because fermion production contributes
negatively to the energy-momentum tensor. When compared with former works on
the subject, our treatment is fully microscopic (namely, we treat fermions by
solving the corresponding Dirac equations) and quantum (in the sense that we
include fermionic loop contributions).
