On the cosmological domain wall problem for the minimally extended supersymmetric standard model

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 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 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