Dynamical dark energy models -- dynamical system approach

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.

RevTeX4, 11 pages, 3 figures; v2 - corrected fig2

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Cited by in corpus (7)

• Dynamics of dark energy
• Bulk viscous cosmology with causal transport theory
• Dissipative or Conservative cosmology with dark energy ?
• FRW Cosmological model with Modified Chaplygin Gas and Dynamical System
• Classification of the FRW universe with a cosmological constant and a perfect fluid of the equation of state $p=w\rho$
• Dynamical System Analysis of Brane Induced Gravity with Tachyon Field
• Paths of Friedmann-Robertson-Walker brane models