Stability of the de-Sitter universe: One-loop nonlocal $f(R)$ gravity

Abstract

With the method of the background field expansion, we investigate the one-loop quantization of the Euclidean nonlocal $f(R)$ model in the de-Sitter universe. We obtain the ghost-free condition (GFC) based on the transformation from the Jordan frame to the Einstein frame and the classical stability condition (CSC) satisfied $f_{RR}^{(0)}-{\varphi }_0{F}_{RR}^{(0)}<0$. We present the on-shell and off-shell one-loop effective action and quantum stability condition (QSC) by utilizing the generalized zeta-function. We find that under the fulfillment of GFC, CSC and QSC are inconsistent.

arXiv comment26 pages,0 figure

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Cited by in corpus (1)

• The stability of the de-Sitter universe in nonlocal gravity