  In this work it is investigated if fermionic sources could be responsible for
accelerated periods during the evolution of a universe where a matter field
would answer for the decelerated period. The self-interaction potential of the
fermionic field is considered as a function of the scalar and pseudo-scalar
invariants. Irreversible processes of energy transfer between the matter and
gravitational fields are also considered. It is shown that the fermionic field
could behave like an inflaton field in the early universe and as dark energy
for an old universe.
