Oscillating and Static Universes from a Single Barotropic Fluid

TL;DR

This paper explores cosmological models with a single barotropic fluid, deriving conditions for static and oscillating universes, and discusses their classical and quantum instabilities.

Contribution

It extends previous work by providing a general analysis of static and oscillating solutions in single-fluid cosmologies, including stability conditions.

Findings

Conditions for static and oscillating solutions derived.

Oscillating solutions are classically unstable due to negative sound speed.

Quantum effects may induce instabilities in these cosmological models.

Abstract

We consider cosmological solutions to general relativity with a single barotropic fluid, where the pressure is a general function of the density, $p = f(\rho)$. We derive conditions for static and oscillating solutions and provide examples, extending earlier work to these simpler and more general single-fluid cosmologies. Generically we expect such solutions to suffer from instabilities, through effects such as quantum fluctuations or tunneling to zero size. We also find a classical instability ("no-go" theorem) for oscillating solutions of a single barotropic perfect fluid due to a necessarily negative squared sound speed.