  We discuss a possibility that the domain wall problem in the next-to-minimal
supersymmetric standard model is alleviated without introducing a small
explicit $Z_3$ breaking term by analyzing the evolution of the singlet scalar
field within an inflationary paradigm. The singlet scalar field which explains
the $\mu$-term tracks a time-varying minimum of the effective potential after
inflation and slowly rolls down to its global minimum if there exist
sufficiently large negative Hubble-induced corrections on the effective
potential for the singlet field, which arise through supergravity. As a
consequence, the whole Universe is confined within a single domain during and
after inflation, which prevents the formation of domain walls. This will
further constrain the history of the early Universe along with the
Higgs-singlet coupling.
