Casimir energy, the cosmological constant and massive gravitons

TL;DR

This paper investigates the cosmological constant as an eigenvalue in quantum gravity, using a variational approach with Gaussian wave functionals, regularization, and renormalization, including the case of massive gravitons.

Contribution

It introduces a variational method with Gaussian wave functionals to analyze the cosmological constant as an eigenvalue, incorporating zeta function regularization and renormalization in a curved background.

Findings

Approximate the Wheeler-De Witt equation to one loop in Schwarzschild background.

Apply zeta function regularization to handle divergences.

Discuss the implications of massive gravitons on the cosmological constant.

Abstract

The cosmological constant appearing in the Wheeler-De Witt equation is considered as an eigenvalue of the associated Sturm-Liouville problem. A variational approach with Gaussian trial wave functionals is used as a method to study such a problem. We approximate the equation to one loop in a Schwarzschild background and a zeta function regularization is involved to handle with divergences. The regularization is closely related to the subtraction procedure appearing in the computation of Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation. The case of massive gravitons is discussed.