Abstract
Motivated by the dark energy issue, the one-loop quantization approach for a family ofrelativistic cosmological theories is discussed in some detail. Specifically, generalf(R) gravity at the one-loop level in a de Sitter universe is investigated, extending a similarprogram developed for the case of pure Einstein gravity. Using generalized zetaregularization, the one-loop effective action is explicitly obtained off shell, which allows usto study in detail the possibility of (de)stabilization of the de Sitter background byquantum effects. The one-loop effective action may also be useful for the study of theconstant curvature black hole nucleation rate and it provides a plausible way of resolvingthe cosmological constant problem.
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