Superinflation, quintessence, and nonsingular cosmologies

The dynamics of a universe dominated by a self-interacting nonminimally coupled scalar field are considered. The structure of the phase space and complete phase portraits are given. New dynamical behaviors include superinflation $(\mathrm{Ḣ}>0),$ avoidance of big bang singularities through classical birth of the universe, and spontaneous entry into and exit from inflation. This model is promising for describing quintessence as a nonminimally coupled scalar field.