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arXiv 2008.02425astro-ph.COgr-qc
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任意功率谱下峰理论中原初黑洞的丰度

Abundance of Primordial Black Holes in Peak Theory for an Arbitrary Power Spectrum

Chul-Moon Yoo, Tomohiro Harada, Shin'ichi Hirano, Kazunori Kohri

备注：
19 pages, 4 figures, PTEP accepted version, errata are reflected. arXiv admin note: text overlap with arXiv:1805.03946
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AI总结：

本文修改了PBH丰度估计程序，通过关注曲率扰动拉普拉斯峰值并解耦环境效应，适用于任意功率谱，并证明k空间顶帽窗口可最小化质量谱缩减。

摘要：

我们修改了arXiv:1805.03946中提出的估计原初黑洞（PBH）丰度的程序，使其能够适用于诸如标度不变平坦功率谱之类的宽功率谱。在新程序中，我们关注曲率扰动拉普拉斯算子$\ riangle ζ$的峰值，并使用每个峰值处的$\ riangle ζ$和$\ riangle \ riangle ζ$的值来指定$ζ$作为径向坐标函数的轮廓，而在arXiv:1805.03946中则使用$ζ$和$\ riangle ζ$的值。新程序将较大尺度的环境效应从PBH丰度的估计中解耦出来。由于消除了由环境效应引起的冗余方差，与arXiv:1805.03946中的先前程序相比，我们获得了更窄的质量谱形状。此外，新程序通过引入窗口函数，使我们能够估计标度不变平坦功率谱下的PBH丰度。尽管最终结果依赖于窗口函数的选择，但我们表明$k$空间顶帽窗口能最小化由窗口函数引起的质量谱的额外缩减。也就是说，$k$空间顶帽窗口在理论PBH估计中具有最小所需性质。我们的程序使得利用考虑非线性关系的合理PBH形成判据，能够计算任意功率谱下的PBH质量谱成为可能。

英文摘要：

We modify the procedure to estimate PBH abundance proposed in arXiv:1805.03946 so that it can be applied to a broad power spectrum such as the scale-invariant flat power spectrum. In the new procedure, we focus on peaks of the Laplacian of the curvature perturbation $\triangle ζ$ and use the values of $\triangle ζ$ and $\triangle \triangle ζ$ at each peak to specify the profile of $ζ$ as a function of the radial coordinate while the values of $ζ$ and $\triangle ζ$ are used in arXiv:1805.03946. The new procedure decouples the larger-scale environmental effect from the estimate of PBH abundance. Because the redundant variance due to the environmental effect is eliminated, we obtain a narrower shape of the mass spectrum compared to the previous procedure in arXiv:1805.03946. Furthermore, the new procedure allows us to estimate PBH abundance for the scale-invariant flat power spectrum by introducing a window function. Although the final result depends on the choice of the window function, we show that the $k$-space tophat window minimizes the extra reduction of the mass spectrum due to the window function. That is, the $k$-space tophat window has the minimum required property in the theoretical PBH estimation. Our procedure makes it possible to calculate the PBH mass spectrum for an arbitrary power spectrum by using a plausible PBH formation criterion with the nonlinear relation taken into account.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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