AI 中文总结
研究超大质量原初黑洞种子质量范围受宇宙微波背景辐射μ畸变限制问题，通过非微扰δN形式，分析四类高斯核族尾部，计算畸变限制的原初黑洞丰度，发现分数势动力学代数尾和重对数正态尾可满足种子丰度需求。
AI 中文摘要
为类星体提供能量的超大质量黑洞难以从恒星质量残骸中生长，因此质量为10^5 - 10^7 M⊙的原初黑洞被视作种子。该质量范围受宇宙微波背景辐射μ畸变限制，高斯扰动下原初黑洞丰度可忽略。本文通过非微扰δN形式规避此限制，分析四类高斯核族，计算畸变限制的原初黑洞丰度，发现代数尾和重对数正态尾可满足种子丰度需求。
英文摘要
Supermassive black holes (SMBHs) powering quasars at $z \gtrsim 6$ are difficult to grow from stellar mass remnants, motivating seeds from primordial black holes (PBHs) with masses $10^5-10^7 M_{\odot}$. This range is constrained by the COBE/FIRAS bound on the CMB $μ$-distortion, which limits the small-scale curvature variance to $σ_ζ^2 \lesssim 10^{-4}$. For Gaussian perturbations, the variance fixes the far tail of the one-point probability distribution function (PDF), making the PBH abundance negligible. We call this the Gaussian barrier. The barrier can be evaded only if the variance probed by the distortion is decoupled from the tail probability controlling collapse. We implement this idea in the non-perturbative $δN$ formalism and relate asymptotic PDF tails to the global shape of the $δN$ map. Four Gaussian-cored families are analyzed: generalized-normal, stretched-exponential, power-law, and log-normal tails. After standardizing each family to unit variance, we impose the FIRAS cap and compute the distortion-limited PBH abundance in the tail-shape parameter space. The ordinary exponential tail produced by standard single-field non-attractor dynamics is still too light to reopen the seed window. Algebraic tails from fractional-potential dynamics, and sufficiently heavy log-normal tails treated as a phenomenological proxy for multiplicative dynamics, can supply seed-relevant abundances while respecting the distortion bound.
Comments14 pages, 6 figures, revised version: additional text and references
