Abstract. In this publication we investigate dynamics of a flat FRW cosmological model with a non-minimally coupled scalar field with the coupling term ξRψ² in the scalar field action. The quadratic potential function V(ψ) ψ² is assumed. All the evolutional paths are visualized and classified in the phase plane, at which the parameter of non-minimal coupling ξ 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 diverge.

Key words: dark energy theory; cosmic singularity; modified gravity

Received 28 March 2009, accepted for publication 12 April 2009
Published 24 April 2009