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

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 $n\ge 4$ spacetime dimension. This generalizes Friedrich's Einstein-Yang-Mills stability results in dimension $n=4$ [ J Differ Geom 34 (1991), 275-345] to all higher dimensions.

65 pages, accepted by Journal of the European Mathematical Society (JEMS). Title changed by adding "Future" in front of "global existence" to emphasize, and minor typos and grammar issues corrected