Dynamical system analysis for accelerating models in non-metricity $f(Q)$ gravity

TL;DR

This paper explores two cosmological models in symmetric teleparallel $f(Q)$ gravity, analyzing their dynamical behavior, stability, and dark energy properties, revealing stable solutions and crossing of the phantom divide line.

Contribution

It introduces two new accelerating cosmological models in $f(Q)$ gravity with dynamical dark energy and performs comprehensive stability and dynamical system analyses.

Findings

Dark energy equation of state crosses the phantom divide line.

Models exhibit violation of energy conditions at late times.

Presence of at least one stable critical point in each model.

Abstract

Two accelerating cosmological models are presented in symmetric teleparallel $f(Q)$ gravity, $Q$ be the non-metricity. The models are constructed based on the assumptions of two different functional forms of $f(Q)$ and a dynamically changing nature of the deceleration parameter that shows transition at $t=2n\pm\sqrt{\frac{4n^2+1}{3}}$, $n$ being a positive constant. In both the models, the equation of state parameter for the dark energy in $f(Q)$ gravity becomes a dynamical quantity and crosses the phantom divide line. The violation of the strong energy condition and the null energy condition at late times are also established. In addition, the dynamical system analysis has been performed and three critical points in each model are identified. In each model, at least one stable node has been observed. To strengthen further, the stability analysis using homogeneous linear perturbations has been performed to ensure the stability of the models.