发表机构
University of Waterloo; Perimeter Institute for Theoretical Physics（滑铁卢大学; 珀尔帖理论物理研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究证明，在保留 Gauss--Bonnet 系数时，二次引力单圈跑动可恢复 de Sitter 解，从而支持由曲率平方耦合量子跑动驱动的暴胀，并预测了与未来 CMB 观测相符的标量倾斜和张量标量比。
AI 中文摘要
近期宇宙微波背景辐射观测所偏好的高标量倾斜，可由纯粹由二次引力曲率平方耦合的量子跑动驱动的暴胀来解释，该暴胀始于跑动的 $R^2$ 耦合极大值处的欧氏四维球面。该极大值仅存在于一种重整化方案中，且一旦包含欧拉迹反常，它便不再是驻点。我们证明，在保留通常被忽略的 Gauss--Bonnet 系数的情况下，标准单圈跑动恢复了缺失的 de Sitter 态：欧拉跑动在唯一的耦合比率下平衡了 $R^2$ 项的尺度依赖性，给出一个对引力约束和紧致欧氏作用量均为驻点的 de Sitter 解，其标量场势能是一个极平坦的山顶（$m^2/H^2\simeq-5\times10^{-10}$），并连接到一个反线性暴胀高原。最后的 $N_*\simeq50$--$60$ 个 $e$-折叠与方案无关，标量倾斜 $n_s\simeq1-4/(3N_*)$，而张量-标量比 $r$ 由增强跑动的物质场数量决定。当前的张量约束排除了纯引力，并设定了最小物质含量，约为 $4\times10^6$ 个共形耦合标量或 $3\times10^5$ 个矢量场——比动量诱导方案所需的少 $2.6$ 倍——而单圈控制直至暴胀结束则设定了约高出十倍的上限。在该窗口内，模型预测 $r\gtrsim0.008$ 且 $0.973\lesssim n_s\lesssim0.978$，处于即将进行的 CMB 偏振巡天可及范围内。
英文摘要
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 ($m^2/H^2\simeq-5\times10^{-10}$) joined to an inverse-linear inflationary plateau. The last $N_*\simeq50$--$60$ $e$-folds are scheme independent, with scalar tilt $n_s\simeq1-4/(3N_*)$, 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 $4\times10^6$ conformally coupled scalars or $3\times10^5$ 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 $r\gtrsim0.008$ with $0.973\lesssim n_s\lesssim0.978$, within reach of upcoming CMB polarization surveys.
Comments6 pages + 8-page appendix, 6 figures, 3 tables; Python code for all figures and numbers
