Toy Model for Eternal Expanding Universe Driven by Quintessence

Recent observations of microwave background and type Ia supernovae (SNe Ia) suggest a space-fiat and accelerated expansion Universe. On the other hand, observations of supernovae 1997ff reveal that the Universe has undergone a decelerating-acceleratingprocess. Combining these two classes of observations, wepresent an eternal expanding Universe toy model driven by quintessence. In this picture, the Universe undergoes an endless sequence of accelerating-decelerating cycles.