Dynamical stability in models where dark matter and dark energy are non-minimally coupled to curvature

This work explores the dynamical stability of cosmological models where dark matter and dark energy can non-minimally couple to spacetime (scalar) curvature. Two different scenarios are presented here. In the initial case, only dark matter sector is coupled to curvature in the presence of a quintessence scalar field. In the second case both dark matter and the quintessence field are coupled to curvature. It is shown that one can get an accelerating expansion phase of the universe in both the cases. The nature of the fixed points show that there can be stable or unstable phases where the curvature coupling vanishes and dark energy and dark matter evolve independently. On the other hand there can be stable accelerating expansion phases where both the components are coupled to curvature.