  We study the response of a classical massless minimally coupled scalar to a
static point scalar charge on de Sitter. By considering explicit solutions of
the problem we conclude that -- even though the dynamics formally admits
dilatation (scaling) symmetry -- the physical scalar field profile necessarily
breaks the symmetry. This is an instance of symmetry breaking in classical
physics due to large infrared effects. The gravitational backreaction, on the
other hand, does respect dilatation symmetry, making this an example of
symmetry non-inheritance phenomenon.
