Curvature and Torsion Quintessence

The issues of quintessence and cosmic acceleration can be discussed in the framework of higher order curvature and torsion theories of gravity. We can define effective pressure and energy density directly connected to the curvature or to the torsion fields and then ask for the conditions to get an accelerated expansion. Exact accelerated expanding solutions can be achieved for several fourth order curvature or torsion theories so that we obtain an alternative scheme to the standard quintessence scalar field, minimally coupled to gravity, usually adopted. We discuss also conformal transformations in order to see the links of quintessence between the Jordan and Einstein frames. Furthermore, we take into account a torsion fluid whose effects become relevant at large scale. Specifically, we investigate a model where a totally antisymmetric torsion field is taken into account discussing the conditions to obtain quintessence. We obtain exact solutions also in this case where dust dominated Friedmann behavior is recovered as soon as torsion effects are not relevant.