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.
Highlights
Special attention is paid to the cases of α = 2 and α = 4, but the analysis can be extended to any other integer positive values of α, including odd values – due to the second law of thermodynamics, these work in the regime of expansion only [7]
Models with α = 2 and α = 4 are studied in detail
The presented analysis can be extended to an arbitrary integer α
Summary
This paper studies a Universe modelled classically as a fluid comprising of a binary mixture of dust with energy density ρd and pressure pd = 0 and a van der Waals gas with equation of state p = nT [1 + n F(T )],. As will be shown shortly, due to the second law of thermodynamics, one must have > 0 so that the entropy is never decreasing With such particle production rate, the particle conservation equation reads off as n = −3n H + n = −3n H (1 − β H α−1). The energy conservation equation for the van der Waals gas and for the dust are ρ + 3H (ρ + p + ) = 0,. Equation (27) can be integrated to get the temperature evolution law in terms of the particle number density:.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
