Collapsing open isotropic universe generated by nonminimally coupled scalar field

TL;DR

This paper studies the evolution of an open isotropic universe driven by a nonminimally coupled scalar field, revealing eventual collapse, potential rebouncing, and finite lifetime depending on initial conditions.

Contribution

It provides new insights into the dynamics of open universes with nonminimal scalar-curvature coupling, especially regarding collapse and rebouncing phenomena.

Findings

Universe collapses to a singularity eventually.

Some cases exhibit rebouncing behavior before collapse.

Universe has finite temporal extent in the future.

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 $\xi$. 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.