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arXiv 2101.10340astro-ph.COgr-qchep-phhep-thmath-phmath.MP
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极值分布与原始黑洞的形成

Extreme-Value Distributions and Primordial Black-Hole Formation

Florian Kuhnel, Dominik J. Schwarz

摘要:

我们认为原始黑洞的形成必须用极值理论来描述。这是早期宇宙中引发黑洞坍缩所需的大能量密度值和坍缩持续时间有限的结果。与最极端的原始密度波动的高斯描述相比,空穴的质量函数更窄,峰值朝向更大的质量。其次,由于极值分布的下降较浅,当将观测到的宇宙大尺度结构的几乎无标度的功率谱外推到原始黑洞质量标度时,原始黑洞的预测丰度被$10^{7}$提升了几个数量级。

英文摘要:

We argue that primordial black-hole formation must be described by means of extreme-value theory. This is a consequence of the large values of the energy density required to initiate the collapse of black holes in the early Universe and the finite duration of their collapse. Compared to the Gaussian description of the most extreme primordial density fluctuations, the holes' mass function is narrower and peaks towards larger masses. Secondly, thanks to the shallower fall-off of extreme-value distributions, the predicted abundance of primordial black holes is boosted by $10^{7}$ orders of magnitude when extrapolating the observed nearly scale-free power spectrum of the cosmic large-scale structure to primordial black-hole mass scales.

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