Abstract

Computations of the primordial black hole (PBH) mass function discussed in the literature have conceptual issues. They stem from the fact that the mass function is a differential quantity and the standard criterion of the PBH formation from the seed primordial fluctuations cannot be directly applied to the computation of the differential quantities. We propose a new criterion of the PBH formation, which is the addition of one extra condition to the existing one. By doing this, we derive a formal expression of the PBH mass function without introducing any ambiguous interpretations that exist in the previous studies. Once the underlying primordial fluctuations are specified, the PBH mass function can be in principle determined by the new formula. As a demonstration of our formulation, we compute the PBH mass function analytically for the case where the perturbations are Gaussian and the space is 1 dimension.

中文翻译：

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撤回题为“在统一框架中违反瘦子数”的论文

摘要

文献中讨论的原始黑洞（PBH）质量函数的计算存在概念性问题。它们源于以下事实：质量函数是一个微分量，并且种子原始波动引起的PBH形成的标准标准不能直接应用于微分量的计算。我们提出了PBH形成的新标准，即在现有条件上增加一个额外条件。通过这样做，我们导出了PBH质量函数的形式表达式，而没有引入先前研究中存在的任何模棱两可的解释。一旦确定了潜在的原始波动，原则上就可以通过新公式确定PBH质量函数。为了说明我们的表述，