Dynamical System Analysis of a Dirac-Born-Infeld Model : A Center Manifold Perspective

TL;DR

This paper analyzes the cosmological dynamics of a Dirac-Born-Infeld dark energy model using center manifold theory, revealing critical points, scaling solutions, and stability properties in a flat universe.

Contribution

It applies a comprehensive dynamical system and center manifold analysis to a string-inspired DBI dark energy model with exponential potential and warp factor.

Findings

Existence of scaling solutions at certain critical points

Complete set of critical points identified

Stability and phase space structure characterized

Abstract

In this paper we present the cosmological dynamics of a perfect fluid and the Dark Energy (DE) component of the Universe, where our model of the dark energy is the string-theoritic Dirac-Born-Infeld (DBI) model. We assume that the potential of the scalar field and the warp factor of the warped throat region of the compact space in the extra dimension for the DBI model are both exponential in nature. In the background of spatially flat Friedman-Robertson-Walker-Lemaitre Universe, the Einstein field equations for the DBI dark energy reduce to a system of autonomous dynamical system. We then perform a dynamical system analysis for this system. Our analysis is motivated by the invariant manifold approach of the mathematical dynamics. In this method, it is possible to reach a definite conclusion even when the critical points of a dynamical system are non-hyperbolic in nature. Since we find the complete set of critical points for this system, the center manifold analysis ensures that our investigation of this model leaves no stone unturned. We find some interesting results such as that for some critical points there are situations where scaling solutions exist. Finally we present various topologically different phase planes and stability diagrams and discuss the corresponding cosmological scenario.