Effective potential for quantum scalar fields on a de Sitter geometry

TL;DR

This paper analyzes the quantum behavior of an O(N) scalar field in de Sitter space using a nonperturbative 1/N-expansion, revealing that self-interactions generate a positive mass and prevent spontaneous symmetry breaking.

Contribution

It provides a nonperturbative calculation of the effective potential for scalar fields in de Sitter space, including renormalization and infrared divergence resolution.

Findings

Field acquires a positive mass due to self-interactions

Infrared divergences are screened by the mass

Spontaneous symmetry breaking is prevented in all dimensions

Abstract

We study the quantum theory of an O(N) scalar field on de Sitter geometry at leading order in a nonperturbative 1/N-expansion. This resums the infinite series of so-called superdaisy loop diagrams. We obtain the de Sitter symmetric solutions of the corresponding, properly renormalized, dynamical field equations and compute the complete effective potential. Because of its self-interactions, the field acquires a strictly positive square mass which screens potential infrared divergences. Moreover, strongly enhanced ultralong-wavelength fluctuations prevent the existence of a spontaneously broken symmetry state in any dimension.