The van der Waals fluid and its role in cosmology

TL;DR

This paper explores a cosmological model using a van der Waals fluid, deriving exact solutions for the universe's expansion, analyzing parameter constraints, and assessing stability, suggesting its relevance for non-eternal inflation.

Contribution

It introduces a novel application of the van der Waals equation of state to cosmology, providing exact solutions and stability analysis for such fluids in the universe.

Findings

Exact solutions for energy density evolution are derived.

Parameter values are constrained based on physical asymptotic behaviors.

The model is stable against small perturbations in relevant cases.

Abstract

We analyze the properties of a generic cosmological fluid described by the van der Waals equation of state. Exact solutions for the energy density evolution are found as implicit functions of the scale factor for a flat Friedmann-Robertson-Walker space-time. The possible values of the free parameter in the van der Waals equation are selected \emph{a posteriori}, in accordance with asymptotic behaviors that are physically relevant. The stability of the model against small perturbations is studied through the hydrodynamic perturbations of the fluid for the relevant cases. It is found that a van der Waals fluid seems appropriate to describe non-eternal inflationary scenarios.