Eur. Phys. J. C (2018) 78: 753
https://doi.org/10.1140/epjc/s10052-018-6225-y

Regular Article - Theoretical Physics

The past and future dynamics of quintom dark energy models

¹ Departamento de Matemáticas, Universidad Católica del Norte, Avda. Angamos 0610, Casilla 1280, Antofagasta, Chile
² Instituto de Ciencias Físicas y Matemáticas, Universidad Austral de Chile, Valdivia, Chile
³ Department of Mathematics and Natural Sciences, Core Curriculum Program, Prince Mohammad Bin Fahd University, Al Khobar, 31952, Kingdom of Saudi Arabia
⁴ Institute of Systems Science, Durban University of Technology, PO Box 1334, Durban, 4000, South Africa
⁵ Departmento de Geomática e Hidráulica, División de Ingeniería, Universidad de Guanajuato, Guanajuato, México

^* e-mail: genly.leon@ucn.cl

Received: 16 August 2018
Accepted: 6 September 2018
Published online: 19 September 2018

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.