Integrable Cosmological Model with van der Waals Gas and Matter Creation

TL;DR

This paper develops an integrable cosmological model incorporating van der Waals gas and matter creation, analyzing its dynamics and conserved quantities to understand its cosmological implications.

Contribution

It introduces a fully integrable dynamical system for cosmology with van der Waals gas and identifies conserved quantities and parameter regimes.

Findings

The model's temperature evolution law is explicitly determined.

A globally conserved Hamiltonian is identified.

Physically meaningful parameter values are characterized.

Abstract

A cosmological model with van der Waals gas and dust has been studied in the context of a three-component autonomous non-linear dynamical system involving the time evolution of the particle number density, the Hubble parameter and the temperature. Due to the presence of a symmetry of the model, the temperature evolution law is determined (in terms of the particle number density) and with this the dynamical system reduces to a two-component one which is fully integrable. The globally conserved Hamiltonian is identified and, in addition to it, some special (second) integrals, defined and conserved on a lower-dimensional manifold, are found. The parameter choices and their implication for the global dynamics in terms of cosmological relevance are comprehensively studied and the physically meaningful parameter values are identified.