About electroweak domain walls in Majoron models

TL;DR

This paper revisits the formation of electroweak domain walls in Majoron models, clarifying the role of instantons and explicit symmetry breaking, and discusses their cosmological implications including potential dark energy contributions.

Contribution

It demonstrates that electroweak instanton effects can be rotated away without explicit B+L breaking, and explores the resulting cosmological impact of Majoron-induced domain walls.

Findings

Instanton effects can be rotated away without explicit B+L breaking.

Tiny instanton-induced Majoron mass can bias wall collapse.

Domain walls do not necessarily lead to cosmological catastrophe.

Abstract

Some time ago it was claimed in "Spontaneous Breaking of Lepton Number and Cosmological Domain Wall Problem" (Phys. Rev. Lett. 122, 151301 (2019)) that non perturbative instantons of the weak interaction $\text{SU}(2)_\text{W}$ lead to the formation of domain walls in Majoron models owing to the anomaly of the spontaneously broken global lepton number $L$ symmetry $\text{U}(1)_L$ with respect to $\text{SU}(2)_\text{W}$. We point out that it has long been known, that this effect can be completely rotated away unless there is a source of explicit $B+L$ breaking present, where $B$ denotes baryon number. We further estimate the tiny instanton induced Majoron mass from $B+L$ breaking and analyze the cosmological impact of such domain walls including possible finite temperature effects. In general this scenario does not lead to a cosmological catastrophe and we demonstrate that the tiny instanton induced mass can act as a bias term to collapse walls induced by a larger source of lepton number breaking. Alternatively this electroweak Majoron could act as dynamical dark energy.