The presence of magnetic fields in the early universe affects the cosmological processes, leading to the distinct signature, which allows constraining their properties and the genesis mechanisms. In this study, we revisit the method to constrain the amplitude of the magnetic fields on small scales in the radiation-dominated era from the abundance of primordial black holes. Constraints in the previous work were based on the fact that the density perturbations sourced by stronger magnetic fields become large enough to gravitationally collapse to form PBHs. However, we demonstrate that this picture is incomplete because magnetic fields also increase the threshold value of the density contrast required for PBH formation. The increase in threshold density contrast is more pronounced on smaller scales, and in extreme cases, it might even prevent PBH production despite the presence of significant magnetic field. Taking into account the relevant physical effects on the magnetized overdense region, we establish an upper-limit on the amplitude of comoving magnetic fields, approximately 0.13-0.15 μG at a scale of 1017Mpc-1. Additionally, we compare our constraints with various small-scale probes.

中文翻译：

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将小尺度原始磁场限制在原始黑洞的丰度中


早期宇宙中磁场的存在会影响宇宙学过程，导致独特的特征，从而可以限制它们的特性和起源机制。在这项研究中，我们重新审视了在辐射主导时代将小尺度磁场振幅限制在原始黑洞的丰度上的方法。之前工作中的约束基于这样一个事实，即由更强磁场产生的密度扰动变得足够大，以至于在引力作用下坍缩形成 PBH。然而，我们证明这张图片是不完整的，因为磁场也增加了 PBH 形成所需的密度对比度的阈值。阈值密度对比度的增加在较小的尺度上更为明显，在极端情况下，尽管存在明显的磁场，它甚至可能阻止 PBH 的产生。考虑到对磁化过密集区域的相关物理影响，我们建立了共动磁场振幅的上限，在 1017Mpc-1 的尺度上约为 0.13-0.15 μG。此外，我们将约束与各种小规模探针进行了比较。