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

One-loop quantum cosmological correction to the gravitational constant in the closed Friedmann-Robertson-Walker universe