Casimir Energy and the Cosmological Constant

TL;DR

This paper investigates the cosmological constant through a quantum gravity approach by treating the Wheeler-De Witt equation as an eigenvalue problem, employing variational methods and zeta function regularization in a Schwarzschild background.

Contribution

It introduces a novel variational method with Gaussian wave functionals to analyze the Wheeler-De Witt equation as a Sturm-Liouville problem for the cosmological constant.

Findings

Eigenvalue spectrum related to the cosmological constant is derived.

Regularization and renormalization techniques are applied to handle divergences.

The approach connects Casimir energy computations to cosmological constant estimation.

Abstract

We regard the Wheeler-De Witt equation as a Sturm-Liouville problem with the cosmological constant considered as the associated eigenvalue. The used method to study such a problem is a variational approach with Gaussian trial wave functionals. We approximate the equation to one loop in a Schwarzschild background. 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.