AI 中文总结
研究原初密度涨落与宇宙结构关系，将游程集形式主义扩展到非高斯涨落，用大偏差原理严格推导，得出随机游走新首次通过时间分布及晕质量函数等新预测，展现大偏差技术在连接暴胀与晚期宇宙观测方面的潜力。
AI 中文摘要
游程集形式主义在原初密度涨落与诸如暗物质晕和空洞等宇宙结构丰度之间建立了关键联系，传统上假设为高斯随机游走。在这项工作中，我们将此框架扩展到分布呈现强烈非高斯尾部的涨落。这种尾部超出了基于矩展开的原初非高斯性微扰方法的范围。我们依靠大偏差原理进行严格的解析推导来解决该问题，适用于研究罕见涨落。我们推导了具有非高斯统计的随机游走的新首次通过时间分布，并获得了晕质量函数的更新预测。我们还研究了与宇宙空洞形成相关的双势垒问题，得出了空洞大小函数的新解析预测，在大尺度上具有更高的精度。我们的结果证明了大偏差技术作为连接通常导致强烈非高斯尾部的暴胀情景与晚期宇宙可观测量之间桥梁的潜力。
英文摘要
The excursion-set formalism provides a key connection between primordial density fluctuations and the abundance of cosmic structures such as dark matter halos and voids, traditionally assuming Gaussian random walks. In this work, we extend this framework to fluctuations whose distribution presents strongly non-Gaussian tails. Such tails are beyond the reach of perturbative approaches to primordial non-Gaussianity based on moment expansion. We address the problem with rigorous, analytical derivations relying on the large deviation principle, suited for the study of rare fluctuations. We derive new first-passage time distributions for random walks with non-Gaussian statistics and obtain updated predictions for the halo mass function. We also study the two-barrier problem relevant to cosmic void formation, leading to a new analytical prediction for the void size function, with improved accuracy on large scales. Our results demonstrate the potential of large deviation techniques as a bridge between inflationary scenarios, often leading to strongly non-Gaussian tails, and late-Universe observables.
Comments35 pages, 6 figures
