On the Cosmological Domain Wall Problem for the Minimally Extended Supersymmetric Standard Model

TL;DR

This paper examines the cosmology of the NMSSM with a Z3 symmetry that provides a μ-term solution via a singlet. It demonstrates that domain walls formed at electroweak breaking require explicit Z3 breaking of at most dimension-5 to avoid cosmological disasters, but such breaking reintroduces the μ problem and destabilizes the hierarchy in minimal Kähler scenarios. By exploring non-minimal Kähler mixing (Giudice-Masiero-like mechanisms), the authors can mitigate destabilising divergences but still face an unresolved naturalness problem due to residual couplings and fine-tuning. Consequently, the NMSSM cannot simultaneously resolve domain-wall cosmology and naturalness without significant fine-tuning, rendering it cosmologically problematic or naturalness-challenged. The work highlights the tension between solving the μ problem and maintaining a stable electroweak scale in the presence of domain walls.

Abstract

We study the cosmology of the Supersymmetric Standard Model augmented by a gauge singlet to solve the $μ$-problem and describe the evolution of the domain walls which are created during electroweak symmetry breaking due to the discrete $Z_{3}$ symmetry in this model. The usual assumption, that non-renormalizable terms induced by gravity (which explicitly break this symmetry) may cause the walls to collapse on a cosmologically safe timescale, is reconsidered. Such terms are constrained by considerations of primordial nucleosynthesis, and also by the fact that by not respecting the $Z_{3}$ symmetry they induce divergences which destabilise the hierarchy and reintroduce the $μ$--problem. We find that, even when the Kähler potential is `non-minimal' (i.e. when the hidden sector couples directly to the visible) the model is either ruled out cosmologically or suffers from a naturalness problem.