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

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 (gravitationally induced) non-renormalisable terms 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 because (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 Kahler 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.