Scalar hair sourced by black holes in de Sitter spacetime grows temporally and spatially on superhorizon scales because a minimally coupled massless scalar field does the same, with the black hole acting as a localized source and carrying outward energy flux.
The Motion of point particles in curved space-time
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On cosmological properties of black-hole hair in linearly coupled scalar-Gauss-Bonnet theory
Scalar hair sourced by black holes in de Sitter spacetime grows temporally and spatially on superhorizon scales because a minimally coupled massless scalar field does the same, with the black hole acting as a localized source and carrying outward energy flux.