Constructing Viable Interacting Dark Matter and Dark Energy Models: A Dynamical Systems Approach

We study the evolution of $k=-1$ FLRW cosmological models for two interacting Dark Matter-Dark Energy Models using dynamical system analysis. Since we are interested in late time evolution, the sign of the interaction term is chosen such that it facilitates the transfer of energy from dark matter to dark energy. We also explore the $k=0$ invariant subspace of these models. We find that both these models have sectors which have a stable fixed point where we can recover an accelerating universe with a negative equation of state. This indicates these can be viable models for our universe. We also rule out certain sectors of these models because they do not give the correct late time observational features. We observe that although we start with a dust-like Dark Matter, its effective equation of state evolves due to its interaction with Dark Energy. As a result, the Dark Matter can display features of stiff matter and exotic matter in the course of evolution.