Dynamics in an invariant manifold of an interacting dark matter and scalar field system

Abstract

We construct a cosmological model in a Friedman-Robertson-Walker universe where dark matter and a dynamically evolving scalar field are coupled by a given interaction term. Through a dynamical systems approach, we investigate the behavior of the kinetic and potential components of the scalar field in this model with the absence of dark matter by considering an invariant manifold that pertains to this scenario. We show that the system in this invariant manifold can be analogous to a mechanical system, provided that the Hubble parameter H is constant, and that this analogy breaks down when H=H(t) due to the system becoming non-autonomous in nature.