Dynamical systems methods and statefinder diagnostic of interacting vacuum energy models

TL;DR

This paper analyzes three interacting dark energy models using dynamical systems and statefinder diagnostics, revealing how interaction strength and variable gravity influence cosmic acceleration and model behavior.

Contribution

It introduces a comprehensive dynamical systems approach to compare interacting vacuum energy models with variable gravitational coupling in a flat universe.

Findings

Models show significant differences with increased interaction strength.

All models exhibit a unique attractor leading to accelerated expansion.

Variable gravitational coupling affects deviation from the standard cosmological model.

Abstract

We study three interacting dark energy models within the framework of four-dimensional General Relativity and a spatially flat Universe. In particular, we first consider two vacuum models where dark energy interacts with dark matter, while relativistic matter as well as baryons are treated as non-interacting fluid components. Secondly, we investigate a third model where the gravitational coupling is assumed to be a slowly-varying function of the Hubble rate and dark energy and dark matter interact as well. We compute the statefinders parameters versus red-shift as well as the critical points and their nature applying dynamical systems methods. In the case of only an interaction term, our main findings indicate that i) significant differences between the models are observed as we increase the strength of the interaction term, and ii) all the models present an unique attractor corresponding to acceleration. On the other hand, when we allow for a variable gravitational coupling, we find that i) the deviation from the concordance model depends of both the strength of gravitational coupling parameter and the interaction term, and ii) there is an unique attractor corresponding to acceleration.