Cosmological dynamics of interacting dark energy and dark matter in viable models of f(R) gravity

Abstract: In this work, we investigate the dynamics of the interacting dark energy and dark matter in viable models of $f(R)$ gravity by using a standard framework of dynamical system analysis. A simple form of the interacting dark energy $Q=3\alpha H\rho_{m}$ is used to study three viable models of $f(R)$ gravity which are consistent with local gravity constraints and satisfying conditions for the cosmological viability. As a result, we find that the fixed points are slightly modified from those obtained in the standard non-interacting analysis of $f(R)$ gravity proposed so far in the literature. In our models of adding this interaction, we find that the dynamical profiles of the universe in the viable $f(R)$ dark energy models are modified by the interaction term as well as their relevant model parameters. Moreover, our results yield the correct cosmological evolution with additional constraint parameter, $\alpha$, from the interacting dark energy.