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arXiv 2411.18525astro-ph.COgr-qchep-th
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单场暴胀模型中 USR 阶段对功率谱的一圈修正的 RG 流重整化

RG-Flow Renormalized One-Loop Corrections to the Power Spectrum in USR Inflation

School of Astronomy, Institute for Research in Fundamental Sciences (IPM)（基础科学研究所天文学院）；Department of Physics, K.N. Toosi University of Technology（K.N.托伊西理工大学物理系）

Haidar Sheikhahmadi, Amin Nassiri-Rad

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39 pages, 2 figure, 3 appendices, typos removed
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AI总结：

研究单场暴胀模型中 USR 阶段长波长 CMB 尺度模式一圈修正的性质。采用重整化群流形式的 UV-IR 正则化方案计算曲率微扰功率谱的重整化一圈贡献，得出功率谱修正与 USR 阶段峰值关系。

摘要：

在具有中间超慢滚（USR）阶段的单场暴胀模型中，长波长 CMB 尺度模式的一圈修正的性质仍是一个活跃的争论话题。在这项工作中，我们对这些曲率微扰功率谱的一圈修正的正则化和重整化进行了详细研究。采用重整化群（RG）流形式中的 UV-IR 组合正则化方案，我们计算了重整化的一圈贡献，包括来自蝌蚪图的贡献，这些贡献来自三次和四次相互作用哈密顿量。这使我们能够有意义地研究耦合常数的跑动，以消除我们研究中出现的发散。我们证明，对功率谱的完全正则化和重整化的分数圈修正是由 USR 阶段结束时的峰值控制的，标度为 $\mathcal{P}_\mathrm{peak} \sim e^{6 \Delta N}$，其中 $\Delta N$ 是 USR 阶段的持续时间。这一结果证实了最初的结论，即如果从 USR 阶段到最终慢滚阶段的转变是瞬时且尖锐的，圈修正可能会变得非微扰地大，这可能会挑战这种原始黑洞形成的暴胀情景的微扰框架。

英文摘要：

The nature of one-loop corrections to long-wavelength CMB-scale modes in single-field inflation models with an intermediate ultra-slow-roll (USR) phase remains a subject of active debate. In this work, we perform a detailed investigation into the regularization and renormalization of these one-loop corrections to the curvature perturbation power spectrum. Employing a combined UV-IR regularization scheme within the renormalization group (RG) flow formalism, we compute the renormalized one-loop contributions, including those from the tadpole diagram, arising from both the cubic and quartic interaction Hamiltonians. This allows us to study meaningfully the running of the coupling constant aiming at removing the divergences appear in our study. We demonstrate that the fully regularized and renormalized fractional loop correction to the power spectrum is controlled by its peak value at the end of the USR phase, scaling as $\mathcal{P}_\mathrm{peak} \sim e^{6 ΔN}$, where $ΔN$ is the duration of the USR phase. This result confirms the original conclusion that loop corrections can become non-perturbatively large if the transition from the USR phase to the final slow-roll phase is instantaneous and sharp, potentially challenging the perturbative framework of such inflationary scenarios for primordial black hole formation.

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