A sharp step on a chaotic potential can enhance primordial curvature fluctuations on smaller scales to the O(10−2) to form primordial black holes (PBHs). The present study discusses an inflationary potential with a sharp step that results in the formation of PBHs in four distinct mass ranges. Also this inflationary model allows the separate consideration of observable parameters n_s and r on the CMB scale from the physics at small scales, where PBHs formation occur. In this work we computed the fractional abundance of PBHs ( fPBH) using the GLMS approximation of peak theory and also the Press–Schechter (PS) formalism. In the two typical mass windows, 10−13M⊙ and 10−11M⊙, fPBH calculated using the GLMS approximation is nearly equal to 1 and that calculated via PS is of 10⁻³. In the other two mass windows 1M⊙ and 6M⊙, fPBH obtained using GLMS approximation is 0.01 and 0.001 respectively, while fPBH calculated via PS formalism yields 10⁻⁵ and 10⁻⁶. The results obtained via GLMS approximation are found to be consistent with observational constraints. A comparative analysis of fPBH obtained using the GLMS perspective and the PS formalism is also included.

中文翻译：

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原初黑洞的形成：通过 GLMS 视角快速探索混沌势


混沌势的急剧进步可以将较小尺度上的原初曲率涨落增强至 O(10−2)，从而形成原初黑洞 (PBH)。本研究讨论了急剧膨胀的潜力，该潜力导致四种不同质量范围内的PBH的形成。此外，这种暴胀模型还允许将 CMB 尺度上的可观测参数 n _s和 r 与发生 PBH 形成的小尺度物理分开考虑。在这项工作中，我们使用峰值理论的 GLMS 近似以及 Press-Schechter (PS) 形式计算了 PBH 的分数丰度 (fPBH)。在两个典型的质量窗口10−13M⊙和10−11M⊙中，使用GLMS近似计算的fPBH几乎等于1，而通过PS计算的fPBH为10 ^-3 。在另外两个质量窗口1M⊙和6M⊙中，使用GLMS近似获得的fPBH分别为0.01和0.001，而通过PS形式计算的fPBH得到10 ^-5和10 ^-6 。通过 GLMS 近似获得的结果与观测约束一致。还包括使用 GLMS 视角和 PS 形式主义获得的 fPBH 的比较分析。