原初黑洞的初始成团：任意局部非高斯性的一般公式
Initial clustering of primordial black holes: A general formulation for arbitrary local non-Gaussianity
- Institute of Science Tokyo（东京科学大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文提出一种适用于任意局部非高斯性的原初黑洞初始成团的一般解析公式，推导出偏置参数，并推广至宽功率谱，为评估初始成团对PBH观测的影响提供了统一理论基础。
AI中文摘要：
由局部型非高斯性（LNG）引起的原初黑洞（PBHs）的初始空间成团可以显著改变对PBH丰度的宇宙学约束。现有的初始PBH成团公式主要局限于小非高斯性或特定区域，缺乏统一的理论框架。在此，我们提出一个适用于任意LNG的PBH两点相关函数的一般解析公式。在假设PBH仅在扰动的大峰值处形成，且长波长模式弱调制短波长（PBH尺度）扰动的局部方差的前提下，我们推导出PBH偏置参数的解析表达式，直接将初始成团与坍缩极限下的原初三谱联系起来。我们通过计算超慢滚暴涨、曲率子（curvaton）和调制再加热（modulated reheating）情景中的偏置参数来展示我们公式的多功能性。我们还将该框架正式推广到宽功率谱，以考虑不同PBH质量尺度之间的相关性。由于我们的公式不依赖于弱或微扰非高斯性假设，我们的结果为评估初始成团对PBH可观测量的影响提供了普遍的理论基础。
英文摘要：
Initial spatial clustering of primordial black holes (PBHs) induced by local-type non-Gaussianity (LNG) can substantially modify cosmological constraints on PBH abundance. Several inflationary scenarios that enhance curvature perturbations at small scales relevant to PBH formation predict LNG that is not necessarily perturbative. Therefore, it is crucial to establish a theoretical framework capable of investigating the initial clustering induced by arbitrary LNG. Here, we present a general analytical formulation for the PBH two-point correlation function applicable to arbitrary LNGs in the alternative approach. Under the assumptions that PBHs form only at the large peaks of perturbations, and that large-scale modes weakly modulate the local variance of small-scale perturbations, we derive an analytic expression for the PBH bias parameter, directly connecting initial clustering to the primordial trispectrum in the collapsed limit. We demonstrate the versatility of our formula by computing the bias parameters in the ultra-slow-roll inflation, curvaton, and modulated reheating scenarios. We also formally generalize the framework to broad power spectra to account for correlations across different PBH mass scales. Because our formulation does not rely on weak or perturbative non-Gaussianity assumptions, our result provides a universal theoretical basis for evaluating initial clustering impact on PBH observables.
