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

TL;DR

This paper employs dynamical system methods to analyze all possible evolution paths of a scalar field cosmology with non-minimal coupling, providing a unified framework for understanding the dynamics leading to accelerated expansion.

Contribution

It introduces a reduction of the scalar field cosmological dynamics to a 3D system using energy variables, allowing a comprehensive analysis of evolution paths and new quintessence scenarios.

Findings

Identification of all admissible evolution paths for the model.

Discovery of a new generic quintessence scenario approaching de Sitter attractor.

Demonstration that non-zero coupling leads to unique dynamical behaviors.

Abstract

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. 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.