AI 中文总结
研究原初黑洞形成中曲率轮廓色散，开发有限作用框架，通过多极傅里叶 - 贝塞尔分解分析，发现其丰度受高斯代价与坍缩阈值增益竞争影响，残余轮廓色散是重要统计成分，能影响丰度估计。
AI 中文摘要
在标准曲率扰动情形下，原初黑洞由视界重新进入后超视界曲率涨落的坍缩形成。其预测丰度对坍缩阈值以及原初曲率轮廓形状指数敏感。本文开发了有限作用框架描述代表性峰值轮廓周围的曲率轮廓色散。利用多极傅里叶 - 贝塞尔分解分离高斯场的局部峰值变量与残余径向和角向变形，并通过高斯作用归一化。应用该形式体系于球形数值坍缩示例以分离径向形状色散的影响。对于有限宽度谱以及存在对数局部非高斯性的情况，计算坍缩阈值作为相干形状变量的函数并结合峰值统计。发现对原初黑洞丰度的主要贡献不一定是平均轮廓，也不是阈值最低的轮廓，而是由实现相干变形的高斯代价与降低坍缩阈值相关的指数增益之间的竞争决定。宽谱和负非高斯性可使罕见形状变形主导丰度。结果表明残余轮廓色散是原初黑洞形成中真正的统计成分，对准确丰度估计在定量上很重要。
英文摘要
In the standard curvature-perturbation scenario, PBHs form from the collapse of superhorizon curvature fluctuations after horizon re-entry. The predicted abundance is exponentially sensitive to the collapse threshold and hence to the shape of the primordial curvature profile. In this work we develop a finite-action framework to describe curvature-profile dispersion around representative peak profiles. Using a multipolar Fourier-Bessel decomposition, we separate the local peak variables of the Gaussian field from residual radial and angular deformations, normalized by their Gaussian action. We apply the formalism to spherical numerical-collapse examples in order to isolate the effect of radial shape dispersion. For finite-width spectra, and in the presence of logarithmic local non-Gaussianity, we compute the collapse threshold as a function of a coherent shape variable and combine the result with peak statistics. We find that the dominant contribution to the PBH abundance is not necessarily the conditional-mean reference profile, nor simply the profile with the lowest threshold. Instead, it is selected by a competition between the Gaussian cost of realizing a coherent deformation and the exponential gain associated with lowering the collapse threshold. Broad spectra and negative non-Gaussianity can make rare shape deformations dominate the abundance. In the examples studied here, the dominant branches can correspond to several-sigma coherent shape fluctuations while enhancing the integrated abundance by orders of magnitude. Equivalently, including shape dispersion can reduce the power-spectrum amplitude required to obtain a fixed PBH abundance. Our results show that residual profile dispersion is a genuine statistical ingredient in PBH formation and can be quantitatively important for accurate abundance estimates.
Comments72 pages and 24 figures. v2: additional numerical results included, references added, and typos corrected
