Phase-space analysis of an anisotropic universe in $f(Q,C)$ gravity

TL;DR

This paper conducts a phase-space analysis of anisotropic cosmologies within $f(Q,C)$ gravity, identifying critical points and stability to understand the universe's evolution from early deceleration to late-time acceleration.

Contribution

It introduces a dynamical systems approach to $f(Q,C)$ gravity models, analyzing their critical points and stability, which is a novel application in anisotropic cosmology.

Findings

Early universe anisotropic variable shows decelerated behavior.

Other parameters indicate accelerated expansion at late times.

Models align with observational data on universe evolution.

Abstract

In this study, we analyze the anisotropic universe in $f(Q,C)$ gravity theory. To achieve this, we consider three specific models of $f(Q,C)$ gravity and rewrite the equations of motion of each model as an autonomous system. We identify and analyze the critical points, examine their stability, and plot phase portraits to illustrate the behavior of each critical point. The evolution of key parameters, including the equation of state (EoS) parameter $w_{eff}$, the deceleration parameter $q$, and the standard density parameters $\Omega_{m}$ and $\Omega_{DE}$, is thoroughly investigated. The anisotropic dynamical variable exhibits decelerated behavior, consistent with the early universe, while the others demonstrate accelerated behavior, aligned with late-time observations across all models.