Torsion, gravity induced chiral symmetry breaking, and cosmological bounce

In this paper, we elaborate and extend our proposal [1] of the cosmological bouncing model in which a chiral condensate violates the null energy condition and induces a bounce. The condensate formation is caused by the gravitational effects that arise in the effective action when the curvature of space-time is nonzero. As the chiral condensation is a vacuum effect, the symmetries of the Friedmann-Robertson-Walker space-time are not violated. We explicitly calculate the spinor effective action in the presence of a background gravitational field up to second order in curvature and with derivative corrections and also derive the initial conditions of the condensate. In addition, a new interaction term between the condensate and the scalar field is introduced that might be relevant for producing the adiabatic perturbations during the contraction phase. The curvature/energy density stays far from Planckian values throughout this evolution.