Nonlinear statistics of primordial black holes from Gaussian curvature perturbations
Nonlinear statistics of primordial black holes from Gaussian curvature perturbations
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DOI：
10.1103/physrevd.101.063520
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发表时间：
2019-12
影响因子：
5
通讯作者：
C. Germani;R. Sheth
中科院分区：
文献类型：
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作者：
C. Germani;R. Sheth
我们发展了由原初曲率扰动的高斯谱产生的原初黑洞的非线性统计。这是通过在以下约束条件下采用压缩函数作为主要统计变量来完成的：a）过密度在点$\vec{x}_0$处具有高峰，B）压实函数在平滑尺度$R$处具有最大值，并且最后，c）、压缩函数振幅在其最大值时高于触发引力坍缩成初始黑洞所需的阈值。密度过大我们的计算允许的事实，即注定要形成PBH的补丁可能有各种轮廓形状和大小。预测的PBH丰度取决于原始波动的功率谱。对于一个非常峰值的功率谱，我们的非线性统计，一个基于线性超密度和一个基于使用曲率扰动，都预测一个狭窄的分布PBH质量和可比的丰度。对于更宽的功率谱，线性超密度统计高估了原始黑洞的丰度，而曲率统计低估了原始黑洞的丰度;对于非常大的平滑尺度，原始黑洞的丰度不再由平均超密度的贡献决定，而是由整个超密度的统计实现决定。
We develop the non-linear statistics of primordial black holes generated by a gaussian spectrum of primordial curvature perturbations. This is done by employing the compaction function as the main statistical variable under the constraints that: a) the over-density has a high peak at a point $\vec{x}_0$, b) the compaction function has a maximum at a smoothing scale $R$, and finally, c) the compaction function amplitude at its maximum is higher than the threshold necessary to trigger a gravitational collapse into a black hole of the initial over-density. Our calculation allows for the fact that the patches which are destined to form PBHs may have a variety of profile shapes and sizes. The predicted PBH abundances depend on the power spectrum of primordial fluctuations. For a very peaked power spectrum, our non-linear statistics, the one based on the linear over-density and the one based on the use of curvature perturbations, all predict a narrow distribution of PBH masses and comparable abundance. For broader power spectra the linear over-density statistics over-estimate the abundance of primordial black holes while the curvature-based approach under-estimates it. Additionally, for very large smoothing scales, the abundance is no longer dominated by the contribution of a mean over-density but rather by the whole statistical realisations of it.