# Late time evolution of a nonminimally coupled scalar field system

## TL;DR

This paper investigates the late-time behavior of a nonminimally coupled scalar field with specific potentials, revealing new stable de-Sitter solutions and asymptotic regimes through autonomous system analysis.

## Contribution

It introduces a novel analysis of late-time dynamics for a nonminimally coupled scalar field with specific potentials, identifying stable de-Sitter solutions previously overlooked.

## Key findings

- Stable de-Sitter solution with $w_{\phi} \simeq -1$
- Constant $G_{eff}$ and scalar field in late-time regime
- New asymptotic regimes identified via autonomous system

## Abstract

We revisit the dynamics of a nonminimally coupled scalar field model in case of $F(\phi)R$ coupling with $F(\phi)= 1-\xi\phi^2 $, and the potentials $V(\phi) = V_0 (1+ \phi^p)^2$, $V(\phi)= V_0 e^{\lambda \phi^2}$. We use an autonomous system to bring out new asymptotic regimes, and find stable de-Sitter solution. Under the chosen functional form of $F(\phi)$ and steep exponential potentials, a true de-Sitter solution is trivially satisfied for which the equation of state $w_{\phi}\simeq -1$, the effective gravitational constant $G_{eff}$ and field $\phi$ are constant that has been missed in the power law case and our previous study.