Cosmology and Quantum Field Theory: A study of the Nambu-Jona-Lasinio Model

We review the Nambu-Jona-Lasinio model (NJL), proposed long time ago, as a four-fermion interaction theory with chiral symmetry. The theory is not renormalizable and presents a symmetry breaking due to quantum corrections which depends on the strength of the coupling constant. We may associate a phase transition with this symmetry breaking, leading from a fermion massless states to fermion condensates. This condensates can be described effectively by a scalar field. We are interested in this paper in the cosmological dynamics of the NJL model, and in the possibility that it can be related to dark energy and/or dark matter, which form up to 95% of the energy content of the universe at present time. We consider exclusively gravitational interaction between the NJL and the SM particles.