Breaking of scaling symmetry by massless scalar on de Sitter

Understand

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.