Collapsing open isotropic universe generated by nonminimally coupled scalar field

Abstract

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 $ϕ_{\rm in}$ is greater than the critical value ${\hat ϕ}_c$=${m_p}/{\sqrt{8πξ(1-6ξ)}}$. 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.