Primordial black hole formation and abundance: contribution from the non-linear relation between the density and curvature perturbation
Primordial black hole formation and abundance: contribution from the non-linear relation between the density and curvature perturbation
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DOI：
10.1088/1475-7516/2019/11/012
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发表时间：
2019-04
影响因子：
6.4
通讯作者：
S. Young;I. Musco;C. Byrnes
中科院分区：
文献类型：
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作者：
S. Young;I. Musco;C. Byrnes
研究了由曲率摄动 z 引起的原初黑洞 (PBH) 的形成和丰度。 ze 和密度对比度 δ 之间的非线性关系意味着，即使 ze 具有精确的高斯分布，也必须考虑影响 PBH 形成的显着非高斯性。利用数值模拟研究PBH形成的临界值和质量，并利用峰值理论计算宇宙在形成PBH时塌缩形成的质量分数。还导出了计算当前 PBH 总丰度和质量函数的形式。研究发现，PBH 的丰度对非线性效应非常敏感，并且功率谱 𝒫ζ 必须是大 𝒪 (2) 的一个因子才能产生相同数量的 PBH，就像使用 ζ 和 δ 之间的线性关系一样（其中精确值取决于区域崩溃并形成 PBH 的临界值）。这也意味着从PBH丰度约束中导出的对小尺度功率谱的约束在相同因素下更弱。
The formation and abundance of primordial black holes (PBHs) arising from the curvature perturbation ζ is studied. The non-linear relation between ζ and the density contrast δ means that, even when ζ has an exactly Gaussian distribution, significant non-Gaussianities affecting PBH formation must be considered. Numerical simulations are used to investigate the critical value and the mass of PBHs which form, and peaks theory is used to calculate the mass fraction of the universe collapsing to form PBHs at the time of formation. A formalism to calculate the total present day PBH abundance and mass function is also derived. It is found that the abundance of PBHs is very sensitive to the non-linear effects, and that the power spectrum 𝒫ζ must be a factor of 𝒪 (2) larger to produce the same number of PBHs as if using the linear relation between ζ and δ (where the exact value depends on the critical value for a region to collapse and form a PBH). This also means that the derived constraints on the small-scale power spectrum from constraints on the abundance of PBHs are weaker by the same factor.