Late time evolution of a nonminimally coupled scalar field system

We revisit the dynamics of a nonminimally coupled scalar field model in case of F ( ϕ ) R coupling with F ( ϕ ) = 1 - ξ ϕ 2 , the potentials V ( ϕ ) = V 0 ( 1 + ϕ p ) 2 and V ( ϕ ) = V 0 e λ ϕ 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 ( ϕ ) and steep exponential potentials, a true de-Sitter solution is trivially satisfied for which the equation of state w ϕ ≃ - 1 , the effective gravitational constant G eff and field ϕ are constant that has been missed in the power law case and our previous study.