Generalized model of interacting dark energy and dark matter: Phase portrait analysis for evolving universe

Abstract

The main aim of this work is to give a suitable explanation of present accelerating universe through an acceptable interactive dynamical cosmological model. A three-fluid cosmological model is introduced in the background of Friedmann–Lemaître–Robertson-Walker asymptotically flat spacetime. This model consists of interactive dark matter and dark energy with baryonic matter, taken as perfect fluid, satisfying barotropic equation of state. We consider dust as the candidate of dark matter. A scalar field [Formula: see text] represents dark energy with potential [Formula: see text]. Einstein’s field equations are utilized to construct a three-dimensional interactive autonomous system by choosing suitable interaction between dark energy and dark matter. We take the interaction kernel as [Formula: see text], where [Formula: see text] indicates the density of dark energy, [Formula: see text] is the interacting constant and [Formula: see text] is Hubble parameter. In order to explain the stability of this system, we obtain some suitable critical points. We analyze stability of obtained critical points to show the different phases of universe and cosmological implications. Surprisingly, we find some stable critical points which represent late-time dark energy-dominated era when a model parameter [Formula: see text] is equal to [Formula: see text]. We introduce a two-dimensional interactive autonomous system and after phase portrait analysis of it, we get several stable points which represent dark energy-dominated era and late-time cosmic acceleration simultaneously. Here, we also demonstrate the variation in interaction at vicinity of phantom barrier [Formula: see text]. From our work, we can also predict the future phase evolution of the universe.