Stability analysis of a f(Q) cosmological model along with EBEC dark matter equation of state

Abstract

This work aim to investigate the mysterious components of the universe, specifically dark energy and dark matter. To characterize the origin of dark energy, we investigate alternative gravity theory to general relativity exhibiting a flat background framework that is based entirely on non-metricity. Specifically, we consider the $f\left(Q\right)$ functional from as $f\left(Q\right)=\gamma Q^2$, where $\gamma$ serves as a free parameter in the model, whereas to describe the dark matter, we assume the relation $p=\alpha \rho +\beta {\rho }^2$ known as the Extended Bose–Einstein Condensate (EBEC) dark matter equation of state. We obtain the motion equations and the continuity relation incorporating both dark matter and dark energy fluid, along with an interaction term, particularly, $I=3bH\rho$, where $b>0$ represents the strength of the energy exchange from dark energy to dark matter. Further, we invoke a set of dimensionless phase space variables that enables us to transform the dynamics of the cosmological system into an autonomous system. Then we perform a detail stability analysis of the considered cosmological model, and we conclude that the cosmological model under consideration effectively captures the dynamics of the universe from a decelerated matter-dominated era to a stable phase of accelerated expansion.