Backreaction of superhorizon scalar field fluctuations on a de Sitter geometry : a renormalisation group perspective

TL;DR

This paper investigates how quantum fluctuations of scalar fields influence the geometry of de Sitter space using a nonperturbative renormalisation group approach, revealing a saturation of curvature due to dynamical mass generation.

Contribution

It introduces a Wilsonian renormalisation group framework to analyze the backreaction of superhorizon scalar fluctuations on de Sitter geometry, including nonminimal couplings and self-interactions.

Findings

Infrared fluctuations induce a nontrivial flow of spacetime curvature.

Dynamical mass generation screens large loop effects, saturating curvature.

Goldstone modes do not affect the infrared flow of curvature.

Abstract

We study the backreaction of gravitationally amplified quantum fluctuations of scalar fields on a classical de Sitter geometry. We formulate the problem in the framework of the Wilsonian renormalisation group, which allows us to treat the scalar field fluctuations in a nonperturbative manner and to follow the renormalisation flow of the spacetime curvature as long wavelength, superhorizon fluctuations are progressively integrated out. For light fields in units of the spacetime curvature, these are described by an effective zero-dimensional field theory and can essentially be computed analytically. A nontrivial flow of the spacetime curvature is induced either by a nonminimal coupling to gravity or by self-interactions. The latter leads to a decrease of the spacetime curvature through loop effects, which, for minimally coupled, massless fields, grow unbounded in the infrared. However, such large loop contributions are eventually screened by the dynamical generation of a nonperturbative, gravitationally induced mass and the renormalisation of the spacetime curvature saturates to a nonzero value. Finally, we show that, in the case of spontaneously broken continuous symmetries, the Goldstone modes do not contribute to the infrared flow of the spacetime curvature, despite being strongly amplified by the gravitational field.