Late time evolution of a nonminimally coupled scalar field system

International audienceWe revisit the dynamics of a nonminimally coupled scalar field model in case of $F(\phi )R$ coupling with $F(\phi )= 1-\xi \phi ^2 $ , the potentials $V(\phi ) = V_0 (1+ \phi ^p)^2$ and $V(\phi )= V_0 e^{\lambda \phi ^2}$ . 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