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.