Symmetry breaking and the Goldstone theorem in de Sitter space

TL;DR

This paper investigates how O(N) symmetry breaking occurs in de Sitter space within a scalar field model, revealing a first-order phase transition and the emergence of pseudo-Goldstone bosons, with implications for defect formation during inflation.

Contribution

It demonstrates symmetry breaking and pseudo-Goldstone boson formation in de Sitter space using the Hartree approximation, highlighting non-analytic phase transition behavior.

Findings

Symmetry can be broken in de Sitter space.

Phase transition can be of first order.

Pseudo-Goldstone bosons acquire mass.

Abstract

We consider an O(N) symmetric scalar field model in the mean field (Hartree) approximation and show that the symmetry can be broken in de Sitter space. We find that the phase transition can be of first order, and that its strength depends non-analytically on the parameters of the model. We also show that the would-be Goldstone bosons acquire a mass, effectively becoming pseudo-Goldstone bosons, thus breaking the O(N) symmetry. Our results imply that topological defects can form during inflation.