Gauss--Bonnet running and the de Sitter saddle of quadratic gravity inflation
Abstract
Inflation driven purely by the quantum running of the curvature-squared couplings of quadratic gravity was shown to accommodate the high scalar tilt favored by recent cosmic microwave background observations, starting from a Euclidean four-sphere at a maximum of the running R2 coupling. That maximum exists only in one renormalization scheme, and is not stationary once the Euler trace anomaly is included. We show that the standard one-loop running, with the usually neglected Gauss--Bonnet coefficient retained, recovers the missing de Sitter state: the Euler running balances the scale dependence of the R2 term at a unique coupling ratio, giving a de Sitter solution that is stationary for the gravitational constraint and for the compact Euclidean action alike, and whose scalaron potential is an extremely flat hilltop (m2/H2≃−5×10−10) joined to an inverse-linear inflationary plateau. The last N*≃50--$60$ e-folds are scheme independent, with scalar tilt ns≃1−4/(3N*), while the tensor-to-scalar ratio, r, is set by the number of matter fields that enhance the running. The current tensor bound excludes pure gravity and sets a minimum matter content, some 4×106 conformally coupled scalars or 3×105 vectors---$2.6$ times fewer than the momentum-induced scheme requires---while one-loop control to the end of inflation sets a maximum about ten times higher. Across that window the model predicts r≳0.008 with 0.973≲ ns≲0.978, within reach of upcoming CMB polarization surveys.
Related
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BibTeX
@misc{liu2026gaussbonnet,
title = {{Gauss--Bonnet running and the de Sitter saddle of quadratic gravity inflation}},
author = {Ruolin Liu and Niayesh Afshordi},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24912},
eprint = {2609.24912},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24912},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Gauss--Bonnet running and the de Sitter saddle of quadratic gravity inflation
AU - Ruolin Liu
AU - Niayesh Afshordi
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24912
UR - https://arxiv.org/abs/2609.24912
AB - Inflation driven purely by the quantum running of the curvature-squared couplings of quadratic gravity was shown to accommodate the high scalar tilt favored by recent cosmic microwave background observations, starting from a Euclidean four-sphere at a maximum of the running R^2 coupling. That maximum exists only in one renormalization scheme, and is not stationary once the Euler trace anomaly is included. We show that the standard one-loop running, with the usually neglected Gauss--Bonnet coefficient retained, recovers the missing de Sitter state: the Euler running balances the scale dependence of the R^2 term at a unique coupling ratio, giving a de Sitter solution that is stationary for the gravitational constraint and for the compact Euclidean action alike, and whose scalaron potential is an extremely flat hilltop (m^2/H^2≃−5×10^−10) joined to an inverse-linear inflationary plateau. The last N_*≃50--$60$ e-folds are scheme independent, with scalar tilt n_s≃1−4/(3N_*), while the tensor-to-scalar ratio, r, is set by the number of matter fields that enhance the running. The current tensor bound excludes pure gravity and sets a minimum matter content, some 4×10^6 conformally coupled scalars or 3×10^5 vectors---$2.6$ times fewer than the momentum-induced scheme requires---while one-loop control to the end of inflation sets a maximum about ten times higher. Across that window the model predicts r≳0.008 with 0.973≲ n_s≲0.978, within reach of upcoming CMB polarization surveys.
ER -