The past and future dynamics of quintom dark energy models

TL;DR

This paper analyzes the dynamics of quintom dark energy models with exponential potentials using advanced mathematical techniques, revealing insights into their phase space behavior, stability, and the influence of curvature.

Contribution

It applies normal forms, center manifold theory, and symmetry analysis to characterize the phase space and stability of quintom cosmologies with exponential potentials.

Findings

Describes the phase space structure near equilibrium points.

Identifies the role of curvature in cosmological dynamics.

Derives conservation laws and algebraic solutions for the models.

Abstract

We study the phase space of the quintom cosmologies for a class of exponential potentials. We combine normal forms expansions and the center manifold theory in order to describe the dynamics near equilibrium sets. Furthermore, we construct the unstable and center manifold of the massless scalar field cosmology motivated by the numerical results given in Lazkoz and Leon (Phys Lett B 638:303. arXiv:astro-ph/0602590, 2006). We study the role of the curvature on the dynamics. Several monotonic functions are defined on relevant invariant sets for the quintom cosmology. Finally, conservation laws of the cosmological field equations and algebraic solutions are determined by using the symmetry analysis and the singularity analysis.