Dynamical dark energy models -- dynamical system approach

TL;DR

This paper analyzes dynamical dark energy models using a phase space approach, providing qualitative insights into their evolution, singularities, and acceleration properties through potential function analysis.

Contribution

It introduces a particle motion analogy in a potential for dynamical dark energy models, enabling qualitative classification and analysis of future singularities and acceleration.

Findings

Potential function analysis classifies evolution paths.

Big rip singularities are characterized in the phase space.

Acceleration regions are visualized on the phase plane.

Abstract

We study the Friedmann-Robertson-Walker model with dynamical dark energy modelled in terms of the equation of state $p_{x}=w_{x}(a(z)) \rho_{x}$ in which the coefficient $w_{x}$ is parameterized by the scale factor $a$ or redshift $z$. We use methods of qualitative analysis of differential equations to investigate the space of all admissible solutions for all initial conditions on the two-dimensional phase plane. We show advantages of representing this dynamics as a motion of a particle in the one-dimensional potential $V(a)$. One of the features of this reduction is the possibility of investigating how typical are big rip singularities in the future evolution of the model. The properties of potential function $V$ can serve as a tool for qualitative classification of all evolution paths. Some important features like resolution of the acceleration problem can be simply visualized as domains on the phase plane. Then one is able to see how large is the class of solutions (labelled by the inset of the initial conditions) leading to the desired property.