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

TL;DR

This paper calculates the one-loop quantum correction to the gravitational constant in a de Sitter universe by leveraging a classical scalar field theory equivalence, revealing how quantum effects can renormalize gravity.

Contribution

It introduces a novel method to compute quantum corrections to gravity using shape invariance and kink solutions in de Sitter cosmology.

Findings

Quantum correction interpreted as a renormalized gravitational constant

Utilizes shape invariance property for calculations

Employs zeta function regularization for precise results

Abstract

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