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In this paper, we show the equivalence between a classical static scalarfield theory and the (closed) de Sitter cosmological model whose potentialrepresents shape invariance property. Based on this equivalence, we calculatethe one-loop quantum cosmological correction to the ground state energy of thekink-like solution in the (closed) de Sitter cosmological model in which thefluctuation potential $V^{\prime\prime}$ has a shape invariance property. It isshown that this type of correction, which yields a renormalized mass in thecase of scalar field theory, may be {\it interpreted} as a renormalizedgravitational constant in the case of (closed) de Sitter cosmological model.Keywords: One-loop correction; kink energy; shape invariance; zeta functionregularization; de Sitter universe.

One-loop quantum cosmological correction to the gravitational constant using the kink solution in de Sitter universe