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

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.