The regular response of a massless minimally coupled scalar to a static point charge on de Sitter necessarily breaks dilatation symmetry, even though its energy-momentum tensor does not.
Quantum Instability of De Sitter Space-time,
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Breaking of scaling symmetry by massless scalar on de Sitter
The regular response of a massless minimally coupled scalar to a static point charge on de Sitter necessarily breaks dilatation symmetry, even though its energy-momentum tensor does not.