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

TL;DR

3-5 sentence high-level summary: The paper develops a one-loop quantization framework for general $f(R)$ gravity on a de Sitter background using generalized $\zeta$-regularization to obtain the off-shell one-loop effective action $\Gamma^{(1)}$, and analyzes the possibility that quantum corrections destabilize the classical de Sitter solution (with $\Lambda_{\rm eff}=\frac{f(R_0)}{2 f'(R_0)}=\frac{R_0}{4}$). For a representative model $f(R)=R-\frac{\mu_1}{R}$ they show that the quantum corrections can generate a minimum of $\Gamma(R_0)$ at a nonzero curvature and may allow tuning toward a vanishing effective cosmological constant; FRW perturbations indicate a growing mode signaling a possible exit from inflation. The work also treats black hole nucleation and entropy in modified gravity through functional determinants on $S^4$ and $S^2 \times S^2$, and provides explicit determinant expressions via zeta functions. Potential extensions to AdS, AdS/CFT, and de Sitter gauged supergravity are discussed as avenues to connect with quantum gravity and cosmology.

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.