Breaking of scaling symmetry by massless scalar on de Sitter

TL;DR

This paper investigates how a classical massless scalar field on de Sitter space breaks scaling symmetry due to infrared effects, despite the underlying equations being scale-invariant, illustrating a classical symmetry breaking phenomenon.

Contribution

It demonstrates that the physical scalar field profile breaks dilatation symmetry on de Sitter space, highlighting a classical symmetry breaking caused by infrared effects.

Findings

Scalar field profile breaks scaling symmetry

Gravitational backreaction preserves dilatation symmetry

Infrared effects induce classical symmetry breaking

Abstract

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.