Effective potential and Goldstone bosons in de Sitter space

TL;DR

This paper studies the nonperturbative infrared effects in the O(N) linear sigma model in de Sitter space, revealing that symmetry breaking and Goldstone bosons are affected by quantum corrections and phase transitions.

Contribution

It provides a nonperturbative analysis of symmetry breaking and Goldstone bosons in de Sitter space using the two-particle irreducible effective action at the Hartree level, including renormalization.

Findings

Spontaneous symmetry breaking is possible in de Sitter space.

Goldstone modes acquire a positive mass due to interaction screening.

A first-order symmetry restoring phase transition occurs as a function of the Hubble parameter.

Abstract

We investigate nonperturbative infrared effects for the O(N) linear sigma model in de Sitter space using the two-particle irreducible effective action at the Hartree truncation level. This approximation resums the infinite series of so-called superdaisy diagrams. For the proper treatment of ultraviolet divergences, we first study the renormalization of this approximation on a general curved background. Then, we calculate radiatively corrected masses and the effective potential. As a result, spontaneous symmetry breaking is possible, on the other hand, the Goldstone modes acquire a positive definite mass term due to the screening effects of interaction. Possible infrared divergence is self-regulated by the mass term. Furthermore, there is a symmetry restoring phase transition as a function of the Hubble parameter. In our approximation, the phase transition is of first order.