Multigravity and spacetime foam

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 the Casimir energy in a curved background. A renormalization procedure is introduced to remove the infinities together with a renormalization group equation.