Quintessence cosmology with coupled complex scalar field

Whereas the recent observations of type Ia supernovae (SNe Ia) reveal the universe is accelerating, we show in this Letter the possibility of a coupled complex scalar field to be quintessence for the source of the accelerating universe. We obtain the main equations which govern the evolution of the universe and rewrite them with the observable quantities. Finally we point out very briefly how future observations may determine the equation of state of quintessence.