Exploring eternal stability with the simple harmonic universe

TL;DR

This paper constructs stable, nonsingular cyclic cosmological models that respect energy conditions and explores their stability, potential decay mechanisms, and implications for an eternal universe.

Contribution

It introduces a class of stable, cyclic universe models with specific matter content and geometric conditions, analyzing their linear and nonlinear stability properties.

Findings

Models are stable under linearized fluctuations.

Casimir energy can prevent nonperturbative decay.

Models provide a framework for eternal universe stability.

Abstract

We construct nonsingular cyclic cosmologies that respect the null energy condition, have a large hierarchy between the minimum and maximum size of the universe, and are stable under linearized fluctuations. The models are supported by a combination of positive curvature, a negative cosmological constant, cosmic strings and matter that at the homogeneous level behaves as a perfect fluid with equation of state -1 < w < -1/3. We investigate analytically the stability of the perturbation equations and discuss the role of parametric resonances and nonlinear corrections. Finally, we argue that Casimir energy contributions associated to the compact spatial slices can become important at short scales and lift nonperturbative decays towards vanishing size. This class of models (particularly in the static limit) can then provide a useful framework for studying the question of the ultimate (meta)stability of an eternal universe.