On the cosmological domain wall problem in supersymmetric models

Many models for dynamical supersymmetry breaking have the domain wall solution of the Kovner-Shifman type and therefore contain the potential cosmological domain wall problem. We show that the degeneracy of the vacua is lifted in any model in which the cosmological constant is fine-tuned to zero through an explicit Z_n^R symmetry breaking constant in the superpotential. In this respect, we do not have to add unnatural non-renormalizable terms which explicitly break the symmetry. We also discuss the conditions for the safe decay of the walls for several concrete examples.