One-loop f(R) gravity in de Sitter universe

TL;DR

This paper investigates the quantum effects of one-loop f(R) gravity in a de Sitter universe, exploring stability, black hole nucleation, and implications for the cosmological constant problem.

Contribution

It extends previous work on Einstein gravity to general f(R) theories, explicitly deriving the one-loop effective action off-shell using zeta regularization.

Findings

Explicit one-loop effective action obtained for f(R) gravity in de Sitter space.

Quantum effects can influence the stability of the de Sitter background.

Potential applications in black hole nucleation and addressing the cosmological constant problem.

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, 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.