One-loop f(R) gravity in de Sitter universe
  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. 
Guido Cognola, Emilio Elizalde, Shin'ichi Nojiri, Sergei D. Odintsov   and Sergio Zerbini