  The accelerated expansion of the Universe is one of the greatest challenges
of modern physics. One candidate to explain this phenomenon is a new field
called dark energy. In this work we have used the Tsallis nonextensive
statistical formulation of the Friedmann equation to explore the
Barboza-Alcaniz and Chevalier-Polarski-Linder parametric dark energy models and
the Wang-Meng and Dalal vacuum decay models. After that, we have discussed the
observational tests and the constraints concerning the Tsallis nonextensive
parameter.
