On the number of instabilities of cosmological solutions in an Einstein-Yang-Mills system

TL;DR

This paper conducts a numerical stability analysis of Einstein-Yang-Mills solutions with a positive cosmological constant, revealing how the number of unstable modes varies with the solution's node number and cosmological constant.

Contribution

It provides the first detailed numerical stability analysis of these solutions, showing how the number of unstable modes changes with parameters and uncovering surprising behavior at certain critical values.

Findings

Number of unstable modes equals the number of nodes for solutions with n=1,2.

The n=3 node solution's unstable modes jump from 3 to 1 at a critical Lambda.

The n=3 node solution with three nodes has only a single unstable mode.

Abstract

A detailed numerical stability analysis of the static, spherically symmetric globally regular solutions of the Einstein-Yang-Mills equations with a positive cosmological constant, Lambda, is carried out. It is found that the number of unstable modes in the even parity sector is n for solutions with n=1,2 nodes as Lambda varies. The solution with n=3 nodes exhibits a rather surprising behaviour in that the number of its unstable modes jumps from 3 to 1 as Lambda crosses (from below) a critical value. In particular the topologically 3-sphere type solution with n=3 nodes has only a single unstable mode.