Phase space analysis of an exponential model in $f(Q)$ gravity including linear dark-sector interactions

Abstract

We present a cosmological analysis of an exponential $f(Q)$ gravity model, within the dynamical systems formalism. Following the method introduced by B\"ohmer \textit{et al} [Universe \textbf{9} no.4, 166 (2023)], the modified Friedmann modified equations are successfully reduced to an autonomous system. Given the exponential form of $f(Q)$, the equilibrium conditions result in transcendental equations, which we approximate to identify the critical points. We therefore perform a general stability analysis of these points in terms of the model parameters. Finally, we extend the model by including a linear dark energy-dark matter interaction, where the equilibrium points are found with their stability properties. The model exhibits the three main domination epochs in the Universe, as well as a non-trivial impact on the late-time de Sitter attractor.