The cosmological constant as an eigenvalue of f(R)-gravity Hamiltonian constraint

In the framework of ADM formalism, it is possible to find out eigenvalues of the WDW equation with the meaning of vacuum states, i.e. cosmological constants, for f® theories of gravity, where f® is a generic analytic function of the Ricci curvature scalar R. The explicit calculation is performed for a Schwarzschild metric where one-loop energy is derived by the zeta function regularization method and a renormalized running Lambda constant is obtained.