  A linear relationship between the Hubble expansion parameter and the time
derivative of the scalar field is assumed in order to derive exact analytic
cosmological solutions to Einstein's gravity with two fluids: a barotropic
perfect fluid of ordinary matter, together with a self-interacting scalar field
fluid accounting for the dark energy in the universe. A priori assumptions
about the functional form of the self-interaction potential or about the scale
factor behavior are not neccessary. These are obtained as outputs of the
assumed linear relationship between the Hubble expansion parameter and the time
derivative of the scalar field. As a consequence only a class of exponential
potentials and their combinations can be treated. The relevance of the
solutions found for the description of the cosmic evolution are discussed in
some detail. The possibility to have superaccelerated expansion within the
context of normal quintessence models is also discussed.
