Torsion, Gravity Induced Chiral Symmetry Breaking and Cosmological Bounce

In this paper, we elaborate and extend our proposal arXiv:2307.16098 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 non-zero. As the chiral condensation is a vacuum effect, the symmetries of the FRW 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.