Background evolution and growth of structures in interacting dark energy through dynamical system analysis

TL;DR

This paper uses dynamical system analysis to study the evolution of interacting dark energy models, revealing stable late-time accelerated solutions and correct matter structure growth at both background and perturbation levels.

Contribution

It introduces a unified dynamical system framework that accounts for matter perturbations, providing new insights into the stability and evolution of interacting dark energy scenarios.

Findings

Identification of critical points representing matter-dominated and dark energy-dominated epochs.

Stable attractors at late times consistent with accelerated expansion and constant matter perturbations.

Natural exit from matter-dominated phase due to saddle points.

Abstract

We apply the formalism of dynamical system analysis to investigate the evolution of interacting dark energy scenarios at the background and perturbation levels in a unified way. Since the resulting dynamical system contains the extra perturbation variable related to the matter overdensity, the critical points of the background analysis split, corresponding to different behavior of matter perturbations, and hence to stability properties. From the combined analysis, we find critical points that describe the non-accelerating matter-dominated epoch with the correct growth of matter structure, and the fact that they are saddle provides the natural exit from this phase. Furthermore, we find stable attractors at late times corresponding to a dark energy-dominated accelerated solution with constant matter perturbations, as required by observations. Thus, interacting cosmology can describe the matter and dark energy epochs correctly, both at the background and perturbation levels, which reveals the capabilities of the interaction.