Scalar field cosmology in the energy phase-space—unified descriptionof dynamics

Abstract

In this letter we apply dynamical system methods to study all evolutional pathsadmissible for all initial conditions of the FRW cosmological model with anon-minimally coupled to gravity scalar field and a barotropic fluid. We choose``energy variables'' as phase variables. We reduce dynamics to a 3-dimensionaldynamical system for an arbitrary potential of the scalar field in the phasespace variables(κϕ̇/61/2H, κV1/2/31/2H, κϕ/61/2).After postulating thepotential parameter Γ as a function of λ (defined as −V′/V) wereduce whole dynamics to a 3-dimensional dynamical system and study evolutionalpaths leading to current accelerating expansion. If we restrict the form of the potential then we will obtain a 2-dimensional dynamical system. We use the dynamical system approach to find a new generic quintessence scenario of approaching to the de Sitter attractor which appears only for the case of non-vanishing coupling constant.