We derive a new parametric class of exact cosmological solutions toBrans-Dicke theory of gravity with a self-interacting scalar field and abarotropic perfect fluid of ordinary matter, by assuming a linear relationshipbetween the Hubble expansion parameter and the time derivative of the scalarfield. As a consequence only a class of exponential potentials and theircombinations can be treated. The relevance of the solutions found for thedescription of the cosmic evolution are discussed in detail. We focus ourdiscussion mainly on the possibility to have superquintessence behavior.
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