New exact cosmological solutions to Brans-Dicke gravity with a self-interacting scalar-field

We derive a new parametric class of exact cosmological solutions to Brans-Dicke theory of gravity with a self-interacting scalar field and a barotropic perfect fluid of ordinary matter, by assuming a 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 detail. We focus our discussion mainly on the possibility to have superquintessence behavior.