Non-minimally coupled scalar field cosmology on the phase plane

TL;DR

This paper analyzes the dynamics of a flat FRW cosmological model with a non-minimally coupled scalar field, showing how the coupling parameter influences evolution paths and can prevent future singularities like the big rip.

Contribution

It provides a detailed phase plane analysis of non-minimally coupled scalar field cosmology with a quadratic potential, highlighting the impact of the coupling constant on global dynamics.

Findings

The non-minimal coupling can prevent the big rip singularity.

Existence of finite scale factor singular points where the Hubble function diverges.

Global dynamics are highly sensitive to changes in the coupling parameter.

Abstract

In this publication we investigate dynamics of a flat FRW cosmological model with a non-minimally coupled scalar field with the coupling term $\xi R \psi^{2}$ in the scalar field action. The quadratic potential function $V(\psi)\propto \psi^{2}$ is assumed. All the evolutional paths are visualized and classified in the phase plane, at which the parameter of non-minimal coupling $\xi$ plays the role of a control parameter. The fragility of global dynamics with respect to changes of the coupling constant is studied in details. We find that the future big rip singularity appearing in the phantom scalar field cosmological models can be avoided due to non-minimal coupling constant effects. We have shown the existence of a finite scale factor singular point (future or past) where the Hubble function as well as its first cosmological time derivative diverges.