Quantum scalar fields in de Sitter space from the nonperturbative renormalization group

TL;DR

This paper uses nonperturbative renormalization group methods to analyze scalar fields in de Sitter space, revealing dimensional reduction effects and their implications for symmetry and mass generation.

Contribution

It introduces a nonperturbative RG approach to de Sitter scalar fields, demonstrating dimensional reduction and connecting it to stochastic and Euclidean zero-mode theories.

Findings

Dimensional reduction to an effective zero-dimensional theory.

Equivalence to late-time stochastic equilibrium state.

Insights into symmetry restoration and mass generation.

Abstract

We investigate scalar field theories in de Sitter space by means of nonperturbative renormalization group techniques. We compute the functional flow equation for the effective potential of O(N) theories in the local potential approximation and we study the onset of curvature-induced effects as quantum fluctuations are progressively integrated out from subhorizon to superhorizon scales. This results in a dimensional reduction of the original action to an effective zero-dimensional Euclidean theory. We show that the latter is equivalent both to the late-time equilibrium state of the stochastic approach of Starobinsky and Yokoyama and to the effective theory for the zero mode on Euclidean de Sitter space. We investigate the immediate consequences of this dimensional reduction: symmetry restoration and dynamical mass generation.