  We discuss the case of massive gravitons and their relation with 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.
