Dynamical analysis of an n−H−T cosmological quintessence real gas model with a general equation of state

Abstract

The cosmological dynamics of a quintessence model based on real gas with general equation of state is presented within the framework of a three-dimensional dynamical system describing the time evolution of the number density, the Hubble parameter, and the temperature. Two global first integrals are found and examples for gas with virial expansion and van der Waals gas are presented. The van der Waals system is completely integrable. In addition to the unbounded trajectories, stemming from the presence of the conserved quantities, stable periodic solutions (closed orbits) also exist under certain conditions and these represent models of a cyclic Universe. The cyclic solutions exhibit regions characterised by inflation and deflation, while the open trajectories are characterised by inflation in a "fly-by" near an unstable critical point.

Integrable cosmological model with van der Waals gas and matter creation

“…In the absence of particle creation (i.e. when Ψ = 0), the above reduces to the well known form given in [26,16,28].…”

“…Methods from dynamical system analysis, see for example [24], [25], are commonly used for the study of various cosmological models. With tools from [26], this paper analyses a simple particle production model the set-up for which has been considered by many authors -see, for example, [4]. The "creation" pressure Π depends only on the energy density ρ and the pressure p, namely Π = −β(ρ + p), where β is a positive constant, that is, Γ = 3βH -see, for example, [7,27].…”

Van der Waals universe with adiabatic matter creation

“…In the absence of particle creation or annihilation (i.e. when β = 0), the above reduces to the well known form given in [9,14,15]. Using the equation of state (1) for the van der Waals gas,…”

“…Note that the temperature is independent of α and β. Equation (27) and its solution are the same as the ones encountered in the case of absence of matter creation or annihilation [9]. The temperature can be excluded so that the system can be reduced to a two-component one:ṅ…”

Dynamic properties of cyclic cosmologies

“…But any direct application of these results to the early physics of our Universe is not justified, since it is precisely in this regime that we should assume that Einstein's general relativity will become invalid due to the quantum gravity effects. In fact, it is a well known result that even some very simple modifications of the field equations of general relativity -which could effectively model the quantum correctionslead to non-singular solutions in which the big-bang is replaced with a bounce: a transition from an earlier phase of contraction to the expansion of the Universe [10,11,12,13,14,15,16,17,18,19,20,21]. Therefore, everything that can actually be stated at this point is only that the early history of the Universe is still not known and that there are no actual reasons to assume that the Universe originated from a primordial singularity.…”