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 $\xi$. In particular we focus on the situation where the initial value for the scalar field $\phi_{\rm in}$ is greater than the critical value ${\hat \phi}_c$=${m_p}/{\sqrt{8\pi\xi(1-6\xi)}}$. The behavior is similar to an open de Sitter universe with $k=-1$ with a negative cosmological constant $\Lambda <0$. 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. 
Takahiro Morishima and Toshifumi Futamase