  We discuss how to extract information about the cosmological constant from
the Wheeler-DeWitt equation, considered as an eigenvalue of a Sturm-Liouville
problem. The equation is approximated to one loop with the help of a
variational approach with Gaussian trial wave functionals. A canonical
decomposition of modes is used to separate transverse-traceless tensors
(graviton) from ghosts and scalar. We show that no ghosts appear in the final
evaluation of the cosmological constant. A zeta function regularization is used
to handle with divergences. A renormalization procedure is introduced to remove
the infinities together with a renormalization group equation. A brief
discussion on the extension to a $f(R)$ theory is considered.
