  In this work we investigate a model for the early Universe in a Bianchi
type-I metric, where the sources of the gravitational field are a fermionic and
a bosonic field, interacting through a Yukawa potential, following the standard
model of elementary particles. It is shown that the fermionic field has a
negative pressure, while the boson has a small positive pressure. The fermionic
field is the responsible for an accelerated regime at early times, but since
the total pressure tends to zero for large times, a transition to a decelerated
regime occurs. Here the Yukawa potential answers for the duration of the
accelerated regime, since by decreasing the value of its coupling constant the
transition accelerated-decelerated occurs in later times. The isotropization
which occurs for late times is due to the presence of the fermionic field as
one of the sources of the gravitational field.
