Non-minimal quintessence with nearly flat potential

We consider Brans-Dicke type nonminimally coupled scalar field as a candidate for dark energy. In the conformally transformed Einstein's frame, our model is a coupled quintessence model. In such models, we consider potentials for the scalar field which satisfy the slow-roll conditions: [(1/V)(dV/d phi)](2) << 1 and (1/V)(d(2)V/d phi(2)) << 1. For such potentials, we show that the equation of state for the scalar field can be described by a universal behaviour, provided the scalar field rolls only in the flat part of the potentials where the slow-roll conditions are satisfied. Our work generalizes the previous work by Scherrer and Sen [7] for minimally coupled scalar field case. We have also studied the observational constraints on the model parameters considering the Supernova and BAO observational data.