Scalar field cosmology in the energy phase-space -- unified description of dynamics

Understand

In this letter we apply dynamical system methods to study all evolutional paths admissible for all initial conditions of the FRW cosmological model with a non-minimally coupled to gravity scalar field and a barotropic fluid.

• We choose "energy variables" as phase variables.
• We reduce dynamics to a 3-dimensional dynamical system for an arbitrary potential of the scalar field in the phase space variables.
• After postulating the potential parameter $\Gamma$ as a function of $\lambda$ (defined as $-V'/V$) we reduce whole dynamics to a 3-dimensional dynamical system and study evolutional paths leading to current accelerating expansion.