Non-minimally coupled scalar field cosmology on the phase plane

In this publication we investigate dynamics of a. at 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) proportional to 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 afinite scale factor singular point (future or past) where the Hubble function as well as its first cosmological time derivative diverge.