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arXiv · 2312.11908

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

Haiyuan Feng·Yi Liao·Rong-Jia Yang
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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 $f^{(0)}_{RR}-\phi_0F^{(0)}_{RR}<0$. 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.

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Haiyuan Feng, Yi Liao, Rong-Jia Yang. 2023-12-19. Stability of the de-Sitter universe: One-loop nonlocal $f(R)$ gravity. https://doi.org/10.1007/jhep05(2024)115

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