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.
On symmetry inheritance of nonminimally coupled scalar fields
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abstract
We present the first symmetry inheritance analysis of fields nonminimally coupled to gravity. In this work we are focused on the real scalar field $\phi$ with nonminimal coupling of the form $\xi\phi^2 R$. Possible cases of the symmetry noninheriting fields are constrained by the properties of the Ricci tensor and the scalar potential. Examples of such spacetimes can be found among those which are "dressed" with the stealth scalar field, a nontrivial scalar field configuration with the vanishing energy-momentum tensor. We classify the scalar field potentials which allow the symmetry noninheriting stealth field configurations on top of the exact solutions of the Einstein's gravitational field equation with the cosmological constant.
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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.