Sigma Model on de Sitter Space

TL;DR

This paper investigates static solutions of the SU(2) sigma model on de Sitter space, revealing a spectrum of solutions with finite energy that are linearly unstable, illustrating key features of non-linear matter-gravity systems.

Contribution

It provides a detailed analysis of spherically symmetric solutions in the sigma model on de Sitter space, highlighting their stability properties and solution structure.

Findings

Existence of a countable set of regular finite-energy solutions.

All solutions exhibit linear instability.

Number of unstable modes increases with energy.

Abstract

We discuss spherically symmetric, static solutions to the SU(2) sigma model on a de Sitter background. Despite of its simplicity this model reflects many of the features exhibited by systems of non-linear matter coupled to gravity e.g. there exists a countable set of regular solutions with finite energy; all of the solutions show linear instability with the number of unstable modes increasing with energy.