Late-time evolution of the Universe within a two-scalar-field cosmological model

TL;DR

This paper analyzes the late-time evolution of the universe in a two-scalar-field cosmological model, identifying solutions that match observed cosmic acceleration and exploring their stability and long-term behavior.

Contribution

It provides a comprehensive dynamical systems analysis of a two-scalar-field model, revealing conditions for viable cosmic evolution scenarios including eternal and temporary acceleration.

Findings

Viable solutions include eternal accelerated expansion and temporary acceleration with constant energy density ratios.

Several parameter regions yield solutions with a matter-dominated era followed by accelerated expansion.

The model's solutions can be stable and consistent with observed late-time cosmic acceleration.

Abstract

We investigate the late-time evolution of the Universe within a cosmological model in which dark matter and dark energy are identified with two interacting scalar fields. Using methods of qualitative analysis of dynamical systems, we identify all cosmological solutions of this model. We show that viable solutions -- in the sense that they correspond to a cosmic evolution in which a long enough matter-dominated era is followed by a current era of accelerated expansion -- can be found in several regions of the parameter space. These solutions can be divided into two categories, namely, solutions that evolve to a state of everlasting accelerated expansion, in which the energy density of the dark-matter field rapidly approaches zero and the evolution becomes entirely dominated by the dark-energy field, and solutions in which the stage of accelerated expansion is temporary and the ratio between the energy densities of dark energy and dark matter tends, asymptotically, to a constant nonzero value.