  Within the scope of a FRW cosmological model we have studied the role of
spinor field in the evolution of the Universe when it is non-minimally coupled
to the gravitational one. We have considered a few types of nonlinearity. It
was found that if the spinor field nonlinearity describes an ordinary matter
such as radiation, the presence of non-minimality becomes essential and leads
to the rapid expansion of the Universe, whereas if the spinor field
nonlinearity describes a dark energy, the evolution of the Universe is
dominated by it and the difference between the minimal and non-minimally
coupled cases become almost indistinguishable.
