  Motivated by the dark energy issue, the one-loop quantization approach for a
family of relativistic cosmological theories is discussed in some detail.
Specifically, general $f(R)$ gravity at the one-loop level in a de Sitter
universe is investigated, extending a similar program developed for the case of
pure Einstein gravity. Using generalized zeta regularization, the one-loop
effective action is explicitly obtained off-shell, what allows to study in
detail the possibility of (de)stabilization of the de Sitter background by
quantum effects. The one-loop effective action maybe useful also for the study
of constant curvature black hole nucleation rate and it provides the plausible
way of resolving the cosmological constant problem.
