论文标题
峰值理论中的原始黑洞的丰度用于任意功率谱
Abundance of Primordial Black Holes in Peak Theory for an Arbitrary Power Spectrum
论文作者
论文摘要
我们修改了估计Arxiv中提出的PBH丰度的过程：1805.03946，以便将其应用于宽阔的功率谱，例如尺度不变的扁平功率谱。在新的过程中，我们重点关注曲率扰动的拉普拉斯峰的峰Arxiv：1805.03946。新程序将大规模的环境效应与PBH丰度的估计值相吻合。由于消除了由于环境效应而引起的冗余方差，因此与ARXIV：1805.03946中的先前程序相比，我们获得了质谱的较窄形状。此外，新的过程使我们能够通过引入窗口函数来估计尺度不变的扁平功率谱的PBH丰度。尽管最终结果取决于窗口函数的选择，但我们表明，由于窗口函数，$ K $ -Space Tophat窗口最小化质谱的额外降低。也就是说，$ k $ -space Tophat窗口具有理论PBH估计中所需的最低属性。我们的程序使通过使用合理的PBH形成标准使用非线性关系来计算任意功率谱的PBH质谱。
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.
