Phase space analysis of interacting and non-interacting models in f(Q, C) gravity

Abstract

Abstract Using a dynamical system method, we have studied a Friedmann-Robertson-Walker (FRW) cosmological model within the context of $f(Q,C)$ gravity, where $Q$ is the non-metricity scalar and $C$ represents the boundary term, considering both interacting and non-interacting models. A set of autonomous equations is derived, and solutions are calculated accordingly. We assessed the critical points obtained from these equations, identified their characteristic values, and explored the physical interpretation of the phase space for this system. Two types of $f(Q,C)$ are assumed to be $(i)$ $f(Q,C)=Q+\alpha Q+\beta C logC$ and $(ii)$ $f(Q,C)=Q+\alpha Q+\frac{\beta}{C}$, where $\alpha$ and $\beta$ are the parameters. In Model I, we obtain two stable critical points, while in Model II, we identified three stable critical points for both interacting and non-interacting models. We look into how the phase space trajectories behave at every critical points. We calculate the values of the physical parameters for both systems at each critical point, indicating the Universe's accelerated expansion.