  The issues of quintessence and cosmic acceleration can be discussed in the
framework of higher order theories of gravity. We can define effective pressure
and energy density directly connected to the Ricci scalar of curvature of a
generic fourth order theory and then ask for the conditions to get an
accelerated expansion. Exact accelerated expanding solutions can be achieved
for several fourth order theories so that we get 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.

General Relativity and Quantum Cosmology