  We study conformal coupling of dark spinor fields to gravity and calculate
the energy density and the pressure of the spinor in FRW spacetime. We consider
the renormalizable potential of the spinor field. In the cases where the field
is proportional to some power of the cosmic scale factor $a(t)$, we determine
the Hubble parameter as a function of the scale factor and find analytic
solutions for $a(t)$ when the spinor field matter dilutes as the universe
expands. We discuss the possibility that both matter- and dark energy-dominated
eras of our universe can be described by the dark spinor.
