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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 pseudoscalar 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.PACS numbers: 98.80.-k, 98.80.Cq

The Universe is modeled as a binary mixture whose constituents are described by a van der Waals fluid and by a dark energy density. The dark energy density is considered either as quintessence or as the Chaplygin gas. The irreversible processes concerning the energy transfer between the van der Waals fluid and the gravitational field are taken into account. This model can simulate ͑a͒ an inflationary period where the acceleration grows exponentially and the van der Waals fluid behaves like an inflaton, ͑b͒ an accelerated period where the acceleration is positive but it decreases and tends to zero whereas the energy density of the van der Waals fluid decays, ͑c͒ a decelerated period which corresponds to a matter dominated period with a non-negative pressure, and ͑d͒ a present accelerated period where the dark energy density outweighs the energy density of the van der Waals fluid.