Abstract. 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, which allows us to study in detail the possibility of (de)stabilization of the de Sitter background by quantum effects. The one-loop effective action may also be useful for the study of the constant curvature black hole nucleation rate and it provides a plausible way of resolving the cosmological constant problem.

Key words: dark energy theory; quantum field theory on curved space

Received 14 January 2005, accepted for publication 14 February 2005
Published 24 February 2005