Dynamics Of Viscous Poly Tropic Gas Dark Energy

In 1998,the Supernova Cosmology Project has simultaneously obtained the results suggesting an unexpected acceleration expansion of the universe.However,the reason for the accelerated expansion of the universe has puzzled scientists.To alleviate this problem,a dynamical dark energy scenario has been proposed with time varying the equation-of state(EoS)parameter w.There are many dark energy models for the dynamical DE scenario which have been introduced to explain the accelerating expansion of universe,such as cosmological constant,quintessence,phantom,quintom,the ’scalar fields’ and viscous polytropic etc.In these models,the polytropic gas model is a hot-spot and keystone to the modern cosmology in recent years.We study the evolution of the viscous polytropic daxk energy model interacting with the dark matter in the Einstein cosmology.The conclusions are shown as follows:We select the viscous polytropic gas model,which state equation is P =Kρ1+1/n-3ζH and the interaction term is Q= 3Hb1ρp + 3Hb2ρm.In order to solve the system of differential equations for some initial conditions,we performed phase space analysis.Setting up 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.By using the dynamic theory to get critical point,we obtain the section of the value range of b1 and b2 where the values of the interaction coefficient of the model n and ζ are given.Appropriate critical points and late time attractors have been found.We find critical stability region around the interaction coefficient.And more,both polytropic gas and viscous polytropic gas can soften the coincidence problem.