Cosmological dynamics of interacting dark energy and dark matter in viable models of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>f</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>R</mml:mi><mml:mo stretchy="false">)</mml:mo></mml:math> gravity
Daris Samart, Bhuddhanubhap Silasan, Phongpichit Channuie
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 $Q=3\ensuremath{\alpha}H{\ensuremath{\rho}}_{m}$ 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 noninteracting 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, $\ensuremath{\alpha}$, from the interacting dark energy.