膨胀不变性如何抑制CMB尺度上曲率扰动的圈修正
How Dilatation Invariance Suppresses Loop Corrections to Curvature Perturbations on CMB Scales
AI总结：
本研究采用舍去空间梯度项的非线性框架，阐明膨胀不变性对CMB尺度曲率扰动圈修正的抑制作用，分析适用于任意暴胀子势与圈阶，且在两种规范下均一致，解决了相关模型中圈修正反作用的争议。
AI中文摘要：
近年来，偏离标准慢滚（SR）暴胀的情形受到越来越多的关注，其中，能大幅增强曲率扰动功率谱的场景常被提出作为产生原初黑洞的机制，原初黑洞可解释部分或全部暗物质。这类模型中存在持续的争议：小尺度上宇宙学扰动的非线性相互作用（即圈修正）是否会变得足够大，从而对CMB尺度产生反作用。本研究采用非线性框架，舍去空间梯度项，以研究超哈勃尺度上的圈修正，重点阐明空间微分同胚不变性，尤其是膨胀不变性（即空间坐标整体重标度下的对称性）在证明CMB功率谱圈修正受抑制中的作用。该分析适用于任意暴胀子势（包括光滑和陡变势）、任意圈阶，只要CMB尺度在SR阶段穿越视界。我们将该结果与文献中采用不同规范选择提出的各类解释进行对比，证明本分析在共动规范和空间平坦规范下均一致；特别地，我们表明在空间平坦规范中，三次相互作用包含一项在陡变极限下发散的项，但该贡献会被四次相互作用完全抵消。
英文摘要：
Departures from standard slow-roll (SR) inflation have attracted increasing interest in recent years. In particular, scenarios that strongly enhance the power spectrum of the curvature perturbation are often proposed as a mechanism for producing primordial black holes, which could account for part or the totality of dark matter. An ongoing debate in these models is whether non-linear interactions of cosmological perturbations on small scales, namely loop corrections, can become sufficiently large to backreact on CMB scales. In this work, we adopt a non-linear framework, dropping spatial-gradient terms, to study loop corrections at super-Hubble scales. Our focus is to clarify the role of spatial-diffeomorphism invariance, especially dilatation invariance, which is the symmetry under overall rescaling of spatial coordinates, in demonstrating the suppression of loop corrections to the CMB power spectrum. This analysis is valid for any inflaton potential, both with smooth and sharp transitions, and at any loop order, as long as the CMB scales cross the horizon during an SR phase. We compare this result with the different explanations proposed in the literature using various gauge choices, and show our analysis is consistent both in the comoving and in the spatially-flat gauges. In particular, we show that in the spatially-flat gauge, the cubic interaction contains a term that diverges in the sharp transition limit. However, this contribution is exactly cancelled by the quartic interaction.
