  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.
