Renormalization group flow and symmetry restoration in de Sitter space

TL;DR

This paper investigates how infrared fluctuations in de Sitter space influence the renormalization group flow of scalar fields, revealing symmetry restoration across dimensions using nonperturbative techniques.

Contribution

It introduces a nonperturbative RG analysis of O(N) scalar theories in de Sitter space, demonstrating symmetry restoration due to infrared effects.

Findings

Infrared fluctuations lead to symmetry restoration in de Sitter space.

The effective potential behaves similarly to Euclidean space with D=0.

Symmetry restoration occurs for all N and dimensions.

Abstract

We compute the renormalization group flow of O(N) scalar field theories in de Sitter space using nonperturbative renormalization group techniques in the local potential approximation. We obtain the flow of the effective potential on superhorizon scales for arbitrary space-time dimension D=d+1. We show that, due to strong infrared fluctuations, the latter is qualitatively similar to the corresponding one in Euclidean space with D=0. It follows that spontaneously broken symmetries are radiatively restored in any space-time dimension and for any value of N.