One loop to rule them all: Perturbativity in the presence of ultra slow-roll dynamics
One loop to rule them all: Perturbativity in the presence of ultra slow-roll dynamics
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DOI：
10.1103/physrevd.109.123550
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发表时间：
2023-05
影响因子：
5
通讯作者：
G. Franciolini;A. Iovino;M. Taoso;A. Urbano
中科院分区：
文献类型：
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作者：
G. Franciolini;A. Iovino;M. Taoso;A. Urbano
我们讨论了具有超慢滚（USR）相位的单场暴胀模型中的微扰问题，该相位适合于产生一阶丰度的原始黑洞（PBHs）。更详细地说，我们施加了一个条件，即由USR动力学增强的短波模式组成的环路修正不会改变曲率摄动的树级功率谱。在我们的分析中，USR阶段之前和之后是普通慢滚（SR）的两个阶段，我们使用瞬时和平滑过渡对SR/USR/SR动力学进行建模。关注与CMB观测相关的尺度，我们发现，根据这些论点，不可能排除通过USR形成PBH的情况，即使在瞬时跃迁的极限下也是如此。然而，我们也发现长模功率谱上短模的环路修正，即使没有大到足以违反摄动要求，仍然是可观的，最重要的是，在平滑SR/USR/SR转换的现实实现中没有被驯化。这使得微扰成为约束USR动力学的有力理论工具。我们将分析扩展到与CMB观测相关的任何尺度。我们发现，如果与树级功率谱相比，短模的环路校正保持在几个百分点以内。然而，我们也发现了现象学相关性的一个值得注意的例外：我们表明，所谓的曲率摄动功率谱的下降是树级计算的产物。
We discuss the issue of perturbativity in single-field inflationary models with a phase of ultra slow-roll (USR) tailor suited to generate an order-one abundance of primordial black holes (PBHs). More in detail, we impose the condition that loop corrections made up of short-wavelength modes enhanced by the USR dynamics do not alter the tree-level power spectrum of curvature perturbations. In our analysis, the USR phase is preceded and followed by two stages of ordinary slow-roll (SR), and we model the resulting SR/USR/SR dynamics using both instantaneous and smooth transitions. Focusing on scales relevant for CMB observations, we find that it is not possible, with these arguments, to rule out the scenario of PBH formation via USR, not even in the limit of instantaneous transition. However, we also find that loop corrections of short modes on the power spectrum of long modes, even though not large enough to violate perturbativity requirements, remain appreciable and, most importantly, are not tamed in realistic realisations of smooth SR/USR/SR transitions. This makes perturbativity a powerful theoretical tool to constrain USR dynamics. We extend the analysis at any scale beyond those relevant for CMB observations. We find that loop corrections of short modes remain within the few percent if compared to the tree-level power spectrum. However, we also find one notable exception of phenomenological relevance: we show that the so-called dip in the power spectrum of curvature perturbation is an artifact of the tree-level computation.