Accelerating behavior from dynamical system analysis parameters

TL;DR

This paper uses dynamical system analysis and observational data to study a modified gravity model, identifying critical points and confirming late-time cosmic acceleration consistent with a stable de Sitter attractor.

Contribution

It reformulates $f(Q)$ gravity into a coupled differential system and applies MCMC with observational data to analyze cosmic evolution and stability.

Findings

Model exhibits quintessence-like behavior today

Converges towards $\\Lambda$CDM at late times

Stable de Sitter attractor confirms acceleration

Abstract

We have performed the dynamical system analysis to obtain the critical point in which, the value of the geometric and dynamical parameters satisfy the late-time cosmic behavior of the Universe. At the outset, the modified Friedmann equations have been reformulated into a system of coupled differential equations to ensure that the minimal set of equations required for a second-order $f(Q)$ gravity. Then these equations are solved numerically to constrain the parameters with Markov Chain Monte Carlo (MCMC) techniques. Cosmic Chronometers (CC) and high-precision Pantheon$^+$ Type Ia Supernovae datasets are used to constrain the parameters. The evolution of key cosmological parameters indicates that the model exhibits quintessence-like behavior at present, with a tendency to converge towards the $\Lambda$CDM model at late-times. The dynamic system analysis provided the critical points that correspond to different phases of the Universe, which are analyzed in detail. The existence of a stable de Sitter attractor confirms the accelerating behavior of the model.