Enhanced Instability of de Sitter Space in Einstein-Gauss-Bonnet Gravity

We show that the addition of a topological Gauss-Bonnet term to the gravitational action can greatly increase the instability of four-dimensional de Sitter space, by favoring the nucleation of black holes. The pair-production rate given by the Euclidean action for the instanton takes the form exp(Delta S) where S is the entropy in Einstein-Gauss-Bonnet theory. The coefficient of the Gauss-Bonnet term in the action sets a stability bound on the curvature of empty de Sitter space. For that coefficient in the low-energy effective action of heterotic string theory, the maximal curvature of de Sitter space is in general much lower than the Planck scale.