Stability Analysis of the Viscous Polytropic Dark Energy Model in Einstein Cosmology**Supported by the National Natural Science Foundation of China under Grant No 10873004, the State Key Development Program for Basic Research Program of China under Grant No 2010CB832803, and the Program for Changjiang Scholars and Innovative Research Team in University under Grant No IRT0964.

Abstract

The viscous polytropic gas model as one model of dark energy is hot-spot and keystone to the modern cosmology. We study the evolution of the viscous polytropic dark energy model interacting with the dark matter in the Einstein cosmology. Setting the autonomous dynamical system for the interacting viscous polytropic dark energy with dark matter and using the phase space analysis method to investigate the dynamical evolution and its critical stability, we find that the viscosity property of the dark energy creates a benefit for the stable critical dynamical evolution of the interaction model between dark matter and dark energy in the flat Friedmann—Robertson—Walker universe and the viscosity of dark energy will soften the coincidence problem just like the interacting dark energy model.