Stability of the de-Sitter universe: one-loop nonlocal f (R) gravity
Haiyuan Feng (Department of Physics, Southern University of Science and Technology, Shenzhen, Guangdong, 518055, China); Yi Liao (Department of Physics, College of Mechanical and Electronic Engineering, Fujian Agriculture and Forestry University, Fuzhou, 350002, China, Department of Materials Science and Engineering, College of Engineering, Southern University of Science and Technology, Shenzhen, 518055, China); Rong-Jia Yang (College of Physical Science and Technology, Hebei University, Baoding, 071002, China)
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 $${f}_{RR}^{\left(0\right)}-{\phi }_{0}{F}_{RR}^{\left(0\right)}<0$$ . 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.