We consider Friedmann cosmologies with minimally coupled scalar field .
Exact solutions are found , many of them elementary , for which the scalar field energy density , \rho _ { f } , and pressure , p _ { f } , obey the equation of state ( EOS ) p _ { f } = w _ { f } \rho _ { f } .
For any constant |w _ { f } | < 1 there exists a two-parameter family of potentials allowing for such solutions ; the range includes , in particular , the quintessence ( -1 < w _ { f } < 0 ) and ‘ dust ’ ( w _ { f } = 0 ) .
The potentials are monotonic and behave either as a power or as an exponent for large values of the field .
For a class of potentials satisfying certain inequalities involving their first and second logarithmic derivatives , the EOS holds in which w _ { f } = w _ { f } ( \varphi ) varies with the field slowly , as compared to the potential .