Global existence and stability of de Sitter-like solutions to the Einstein-Yang-Mills equations in spacetime dimensions $n\geq 4$

Abstract

We establish the global existence and stability to the future of non-linear perturbation of de Sitter-like solutions to the Einstein-Yang-Mills system in n ≥ 4 spacetime dimension. This generalizes Friedrich's Einstein-Yang-Mills stability results in dimension n = 4 [11] to all higher dimensions.1 In this article, we use abstract index notations, see §2.1. 2 The Yang-Mills curvature Fab is globally defined when viewed as taking values in the adjoint bundle. 3 In fact, we will only make use of the future half [0, ∞) × Σ of M n given by [0, ∞) × Σ. 4 See the references [13, 28] for a more detailed introduction to de Sitter spacetime.