发表机构
Hunan Institute of Technology; SGT University; University of Chinese Academy of Sciences; Hainan University; Tongji University; Institute for Advanced Study of Tongji University; Asia Pacific Center for Theoretical Physics; The University of Tokyo; Yangzhou University（湖南理工学院; SGT大学; 中国科学院大学; 海南大学; 同济大学; 同济大学高等研究院; 亚太理论物理中心; 东京大学; 扬州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文通过数值相对论模拟研究刚性热历史中有限宽度功率谱下原初黑洞的坍缩阈值，发现阈值随宽度和状态方程参数增大，并影响暗物质丰度与引力波信号。
AI 中文摘要
我们研究了在状态方程参数 ${\rm w}\geq1/3$ 的时期重新进入视界的大型原初扰动所导致的原初黑洞（PBH）的形成过程。我们考虑一个有限宽度 $\Delta$ 的对数正态曲率功率谱，并通过自引力理想流体的数值相对论模拟来确定坍缩阈值。针对五个 $\rm w$ 值和五个谱宽度进行了阈值扫描，并将所得的数值阈值用于PBH丰度和标量诱导引力波（SIGW）的计算中。为了比较，我们还评估了半解析的 $q$ 函数方法。该方法在接近辐射主导时期以及近单色谱的情况下能重现数值趋势，但对于更刚性背景中的一般有限宽度谱，它并非可靠的阈值估计器。我们展示了坍缩阈值如何随 $\Delta$ 和 $\rm w$ 的增加而增大，这改变了PBH构成全部暗物质所需的曲率扰动幅度，并因此影响了伴随的SIGW信号的归一化。
英文摘要
We study the formation of primordial black holes (PBHs) from large primordial perturbations that re-enter the horizon during an epoch with equation of state ${\rm w}\geq1/3$. We consider a log-normal curvature power spectrum of finite width $Δ$ and determine the collapse amplitude by numerical-relativity simulations of a self-gravitating perfect fluid. Threshold scans are performed for five values of $\rm w$ and five spectral widths, and the resulting numerical thresholds are used in the PBH abundance and scalar-induced gravitational-wave (SIGW) calculations. For comparison, we also evaluate the semi-analytical $q$-function prescription. It reproduces the numerical trend close to radiation domination and for nearly monochromatic profiles, but it is not a reliable threshold estimator for generic finite-width profiles in stiffer backgrounds. We show how collapse thresholds increase with both $Δ$ and $\rm w$, changing the curvature amplitude required for PBHs to constitute all of the dark matter and, consequently, the normalization of the accompanying SIGW signal.
Comments21 pages, 12 figures, 2 tables
