Stability analysis of cosmological models coupled minimally with scalar field in $f(Q)$ gravity

TL;DR

This paper investigates the stability and dynamics of a cosmological model in $f(Q)$ gravity with a linear form, analyzing critical points, cosmic acceleration, and stability to understand its viability as a dark energy model.

Contribution

It introduces a dynamical system analysis of $f(Q)$ gravity with interaction between dark matter and dark energy, identifying critical points and stability conditions for accelerated expansion.

Findings

The model exhibits accelerated expansion with $q=-1$ and $ ext{EoS}=-1$, consistent with $ ext{Lambda}$CDM.

Six critical points are identified in the phase space analysis.

The model is shown to be classically and quantum mechanically stable under certain parameter ranges.

Abstract

In this work, in the framework of dynamical system analysis, we focus on the study of the accelerated expansion of the Universe of $f(Q)$ gravity theory where $Q$ be the non-metricity that describes the gravitational interaction. We consider the linear form of $f(Q)$ gravity i.e. $f(Q)=-\alpha_{1}Q-\alpha_{2}$ where $\alpha_{1}$ and $\alpha_{2}$ are constants. We consider an interaction between dark matter (DM) and dark energy (DE) in $f(Q)$ gravity. To reduce the modified Friedmann equations to an autonomous system of first-order ordinary differential equations, we introduce some dimensionless new variables. The nature of the critical points are discussed by finding the eigenvalues of the Jacobian matrix. We get six critical points for interacting DE model. We also analyze the density parameter, equation of state (EoS) parameter and deceleration parameter and draw their plots and we conclude that for some suitable range of the parameters $\lambda$ and $\alpha$, the value of the deceleration parameter is $q=-1$ which shows that the expansion of Universe is accelerating and the value of EoS parameter is $\omega_{\phi}=-1$ which shows that the model is $\Lambda$CDM model. Finally, we discussed the classical as well as quantum stability of the model.