Study of dynamical systems and large-scale structure

TL;DR

This paper uses dynamical systems techniques to analyze large-scale cosmic structures within dark energy models inspired by QCD, identifying fixed points that correspond to different cosmic eras.

Contribution

It introduces a dynamical systems framework for two interaction models in dark energy, revealing stability properties and cosmic evolution implications.

Findings

Identification of fixed points for different cosmic eras

Demonstration of model viability for dark sector interactions

Analysis of stability and transition between cosmic phases

Abstract

In this study, we employ dynamical systems methods to analyse the large-scale structure by considering two distinct interaction models (linear and non-linear) within the dark sector, associated with a specific dynamical dark energy model inspired by the Veneziano ghost theory in quantum chromodynamics (QCD). In these models, the dark energy density ($\rho_{DE}$) varies with the Hubble parameter ($H$), expressed as $\rho_{DE} = \alpha H + \beta H^2$. After defining the dimensionless parameters, we present autonomous equations that allow us to find the trace $\text{Tr}(J)$ and the determinant $D(J)$. With these solutions, we demonstrate the presence of unstable, saddle, and stable fixed points, corresponding to the radiation-, matter-, and dark-energy-dominated eras, respectively. Our results suggest that these models are theoretically viable for representing the interaction between dark sector fluids.