Dynamical Stability and Geometrical Diagnostic of the Power Law K-Essence Dark Energy Model with Interaction

Bo-Hai Chen,Nan Zhang,Ya-Bo Wu,Wei Dong,Dong-Fang Xu

doi:10.3390/universe6120244

Abstract

We investigate the cosmological evolution of the power law k-essence dark energy (DE) model with interaction in FRWL spacetime with the Lagrangian that contains a kinetic function F(X)=−X+X. Concretely, the cosmological evolution in this model are discussed by the autonomous dynamical system and its critical points, together with the corresponding cosmological quantities, such as Ωϕ, wϕ, cs2, and q, are calculated at each critical point. The evolutionary trajectories are drawn in order to show the dynamical process on the phases plan around the critical points. The result that we obtained indicates that there are four dynamical attractors, and all of them correspond to an accelerating expansion of universe for certain potential parameter and coupling parameter. Besides that, the geometrical diagnostic by the statefinder hierarchy S3(1) and S4(1) of this scalar field model are numerically obtained by the phase components, as an extended null diagnostic for the cosmological constant. This diagnostic shows that both the potential parameter λ and interaction parameter α play important roles in the evolution of the statefinder hierarchy.

Highlights

There are two important stages in cosmology, the early inflation and the late time accelerated expansion
The geometrical diagnostic by the statefinder hierarchy S3 and S4 of this scalar field model are numerically obtained by the phase components, as an extended null diagnostic for the cosmological constant
The accelerating expansion is based on the observations on the luminosity-redshift relation of distant Ia supernovas [1,2], Cosmic Microwave Background [3], and Baryon Acoustic Oscillations [4], which indicate that the current energy density in the universe is composed by 68.3% dark energy (DE), 26.8% dark matter (DM), and 4.9% baryons [5] in order to drive the late time acceleration approximately

Summary

Introduction

There are two important stages in cosmology, the early inflation and the late time accelerated expansion. The approximation of the potential in scalar field dark energy models are discussed in [32], with both canonical and noncanonical kinetic terms In another aspect, from the matter clustering properties, dark matter (DM) and dark energy are not the same substance; there are researches regarding the interactions between them, even some nonlinear interaction forms [33,34,35,36,37], which can provide a mechanism for generating acceleration. S4 are analyzed to the scalar dark energy model by the phase components (the auxiliary variables) in the autonomous equations, unlike the method that was mentioned before, which depends on the cosmological quantities It shows that the hierarchies are varied from two parameters λ and α by the trajectories. We close with a few concluding remarks in the fifth section

The Power Law K-Essence Dark Energy Model and Its Stability Analysis

The Geometric Diagnostic of Statefinder Hierarchy

Conclusions