Collapsing open isotropic universe generated by nonminimally coupled scalar field

We investigated the behavior of an open isotropic universe generated by a scalar field which couples with background curvature nonminimally with the coupling constant ξ. In particular we focus on the situation where the initial value for the scalar field φin is greater than the critical value φ̂c=mp/8πξ(1−6ξ). The behavior is similar to an open de Sitter universe with k=−1 with a negative cosmological constant Λ<0. It is found that the universe will collapse eventually to a singularity and thus has a finite extent in time in the future. Furthermore, there are some cases which shows a rebouncing behavior before the final collapse.