从旧到新的 Starobinsky 暴胀
From the Old to the New Starobinsky Inflation
- School of Science, Huzhou Normal University（湖州师范学院理学院）
- Center for Gravitational Physics and Quantum Information, Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所引力物理与量子信息中心）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文统一了 Starobinsky 暴胀的迹反常与 $R^2$ 表述，发现反常修正由 $aN_*/(18b)$ 控制，使观测谱指数仅需 $b/a\simeq35$，并给出张标比降低约 17% 的定量特征。
中文摘要 AI 辅助
Starobinsky 最初的暴胀模型由共形场的迹反常驱动，其 $R+R^2$（标量子）表述通常被分开处理。由反常驱动的原始演化将早期由欧拉反常支持的 de Sitter 相连接到标量子区域，在该区域中可观测模式离开视界。基于这一已知的背景连接，我们在精确背景上计算标量和张量谱，发现反常修正由 $aN_*/(18b)$ 控制，其中 $a$ 和 $b$ 分别是欧拉反常和 $R^2$ 系数，$N_*$ 是枢轴标度退出视界后的 e 折叠数；当该参数为零时恢复标量子暴胀。在 $N_*=60$ 处观测到的谱指数仅要求 $b/a\simeq35$，而非早期实现所需的 $b/a\gtrsim10^9$。在此基准下，固定 $N_*$ 时标量谱比标量子暴胀更红，且固定谱指数时张标比约低 17%，这是反常的定量特征。对于最小引力再加热，$N_*\simeq53$，当 $b/a\gtrsim35$ 时谱指数保持在 Planck 值的 $1\sigma$ 范围内。在 de Sitter 分析中，Weyl 耦合的有限范围排除了额外的实自旋-2 极点，并保持因果响应衰减。配套论文给出了完整分析。
英文摘要
Starobinsky's original model of inflation, driven by the trace anomaly of conformal fields, and its $R+R^2$ (scalaron) formulation are often treated separately. The original anomaly-driven evolution connects an early de Sitter phase supported by the Euler anomaly to a scalaron regime, where the observable modes leave the horizon. Building on this known background connection, we compute the scalar and tensor spectra on the exact background and find that the anomaly corrections are controlled by $aN_*/(18b)$, where $a$ and $b$ are the Euler-anomaly and $R^2$ coefficients and $N_*$ the number of e-folds after the pivot exits the horizon; scalaron inflation is recovered as this parameter vanishes. The observed tilt at $N_*=60$ then requires only $b/a\simeq35$, rather than the $b/a\gtrsim10^9$ of early realizations. At this benchmark the scalar spectrum is redder than in scalaron inflation at fixed $N_*$, and the tensor-to-scalar ratio is about 17% lower at fixed tilt, a quantitative signature of the anomaly. For minimal gravitational reheating, $N_*\simeq53$, the tilt remains within $1σ$ of the Planck value for $b/a\gtrsim35$. In the de Sitter analysis, a finite range of the Weyl coupling excludes an extra real spin-two pole and keeps the causal response decaying. A companion paper gives the full analysis.
