Generalized Scalar Field Cosmologies: A Global Dynamical Systems Formulation

TL;DR

This paper develops a comprehensive dynamical systems framework to analyze scalar field cosmologies with arbitrary potentials and couplings, revealing diverse stability properties and solution behaviors in FLRW and Bianchi I models.

Contribution

It introduces a global phase-space formulation for scalar field cosmologies, enabling analysis of stability and dynamics across various solutions and regimes.

Findings

Identification of multiple stable and unstable equilibrium points.

Analysis of scalar field divergence regimes.

Rich variety of cosmological solution behaviors.

Abstract

Local and global phase-space descriptions and averaging methods are used to find qualitative features of solutions for the FLRW and the Bianchi I metrics in the context of scalar field cosmologies with arbitrary potentials and arbitrary couplings to matter. The stability of the equilibrium points in a phase-space as well as the dynamics in the regime where the scalar field diverges are studied. Equilibrium points that represent some solutions of cosmological interest such as: several types of scaling solutions, a kinetic dominated solution representing a stiff fluid, a solution dominated by an effective energy density of geometric origin, a quintessence scalar field dominated solution, the vacuum de Sitter solution associated to the minimum of the potential, and a non-interacting matter dominated solution are obtained. All reveal a very rich cosmological phenomenology.