  We have found that supersymmetry (SUSY) in curved space is broken softly. It
is also found that Pauli-Villars regularization preserves the remaining
symmetry, softly broken SUSY. Using it we computed the one-loop effective
potential along a (classical) flat direction in a Wess-Zumino model in de
Sitter space. The analysis is relevant to the Affleck-Dine mechanism for
baryogenesis. The effective potential is unbounded from below:
$V_{eff}(\phi)\to -3g^2H^2\phi ^2 ln \phi ^2 /16\pi ^2$, where $\phi$ is the
scalar field along the flat direction, g is a typical coupling constant, and H
is the Hubble parameter. This is identical with the effective potential which
is obtained by using proper-time cutoff regularization. Since proper-time
cutoff regularization is exact even at the large curvature region, the
effective potential possesses softly broken SUSY and reliability in the large
curvature region.
