  In this paper, we calculate the one-loop quantum cosmological corrections to
the kink energy in the closed Friedmann-Robertson-Walker universe in which the
fluctuation potential $V^{\prime\prime}$ has a shape invariance property. We
use the generalized zeta function regularization method to implement our setup
for describing quantum kink-like states. It is conjectured that the corrections
lead to the renormalized gravitational constant.
