Phase space analysis and singularity classification for linearly interacting dark energy models

TL;DR

This paper uses phase space analysis to classify singularities and late-time behaviors in linearly interacting dark energy models with various equations of state, identifying conditions for stable de Sitter attractors.

Contribution

It provides a qualitative analysis of late-time attractors in interacting dark energy models with non-ideal equations of state, extending understanding of their stability and singularity properties.

Findings

Late-time attractors correspond to de Sitter universes with negative deceleration.

Deviation from ideal fluid does not affect attractor stability or cosmological parameters, except for the Hubble function.

Singularity in the dark energy equation of state parameter is not possible in these models.

Abstract

In this paper, applying the Hartman-Grobman theorem we carry out a qualitative late-time analysis of some unified dark energy-matter Friedmann cosmological models, where the two interact through linear energy exchanges, and the dark energy fluid obeys to the dynamical equation of state of Redlich-Kwong, Modified Berthelot, and Dieterici respectively. The identification of appropriate late-time attractors allows to restrict the range of validity of the free parameters of the models under investigation. In particular, we prove that the late-time attractors which support a negative deceleration parameter correspond to a de Sitter universe. We show that the strength of deviation from an ideal fluid for the dark energy does not influence the stability of the late-time attractors, as well as the values of all the cosmological parameters at equilibrium, but for the Hubble function (which represents the age of the universe). Our analysis also shows that a singularity in the effective equation of state parameter for the dark energy fluid is not possible within this class of models.