Multigravity and Space Time Foam

TL;DR

This paper explores a multigravity framework for spacetime foam, using variational methods and zeta function regularization to estimate the cosmological constant as an eigenvalue problem in a curved background.

Contribution

It introduces a novel multigravity approach to spacetime foam and applies a variational method with Gaussian wave functionals to compute the cosmological constant.

Findings

Approximate eigenvalue calculation for the cosmological constant.

Application of zeta function regularization to handle divergences.

Use of renormalization group equations to remove infinities.

Abstract

We consider a multigravity approach to spacetime foam. As an application we give indications on the computation of the cosmological constant, considered as an eigenvalue of a 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.