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

A detailed numerical stability analysis of the static, spherically symmetric globally regular solutions of the Einstein-Yang-Mills equations with a positive cosmological constant, Λ, 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 Λ 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 Λ crosses (from below) a critical value. In particular the topologically 3-sphere type solution with n = 3 nodes has only a single unstable mode.