Van der Waals Universe with Adiabatic Matter Creation

Abstract

A FRWL cosmological model with perfect fluid comprising of van der Waals gas and dust has been studied in the context of dynamical analysis of a three-component autonomous non-linear dynamical system for the particle number density $n$, the Hubble parameter $H$, and the temperature $T$. Perfect fluid isentropic particle creation at rate proportional to an integer power $\alpha$ of $H$ has been incorporated. The existence of a global first integral allows the determination of the temperature evolution law and hence the reduction of the dynamical system to a two-component one. Special attention is paid to the cases of $\alpha = 2$ and $\alpha = 4$ and these are illustrated with numerical examples. The global dynamics is comprehensively studied for different choices of the values of the physical parameters of the model. Trajectories in the $(n, H)$ phase space are identified for which temporary inflationary regime exists.