发表机构
Lunit Inc.; Izmir Institute of Technology; Università di Padova（Lunit公司; 伊兹密尔理工大学; 帕多瓦大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究建立随机气泡完成时间涨落的首达框架，揭示德西特膨胀下有限转变时长产生红外敏感矩层级，且双谱比功率谱更敏感，并给出解析白噪声极限。
AI 中文摘要
随机气泡成核使得一阶相变的局部完成时间成为一个随机空间场。我们研究了其在闵可夫斯基背景和德西特背景下的功率谱和等边双谱，特别关注有限转变持续时间所带来的红外后果。在永恒延展的德西特历史中，遥远过去成核的稀有气泡会产生一个古老气泡尾部，该尾部生成一系列红外敏感的空间矩层级。对于两点函数，第一个有限$k$修正项在$H/\beta=1/5$处变得对尾部敏感，而主导矩在$H/\beta=1/3$处变得奇异。相应的三点阈值分别为$H/\beta=1/8$和$1/6$，表明双谱比功率谱对红外更敏感。然而，对于任何有限的起始时间，古老气泡尾部被截断，所有空间矩保持有限，严格的红外谱恢复解析白噪声极限${\cal P}_\tau\propto k^3$和${\cal B}^{\rm eq}_\tau\propto k^6$。永恒背景阈值反而控制矩系数对持续时间的依赖性以及进入中间尾部敏感区的交叉，这与我们的数值计算一致。我们进一步表明，成核历史的时间局域化提供了古老气泡尾部的平滑调节器，并恢复了相同的解析红外极限。这些结果建立了完成时间涨落的一般首达框架，并阐明了德西特膨胀如何生成与曲率扰动和非高斯性相关的不同功率谱和双谱红外层级。
英文摘要
Stochastic bubble nucleation makes the local completion time of a first-order phase transition a random spatial field. We study its power spectrum and equilateral bispectrum in Minkowski and de Sitter backgrounds, with particular emphasis on the infrared consequences of a finite transition duration. In an eternally extended de Sitter history, rare bubbles nucleated in the remote past generate an ancient-bubble tail that produces a hierarchy of infrared-sensitive spatial moments. For the two-point function, the first finite-$k$ correction becomes tail sensitive at $H/β=1/5$, while the leading moment becomes singular at $H/β=1/3$. The corresponding three-point thresholds are $H/β=1/8$ and $1/6$, showing that the bispectrum is more infrared sensitive than the power spectrum. For any finite starting time, however, the ancient-bubble tail is cut off, all spatial moments remain finite, and the strict infrared spectra recover the analytic white-noise limits ${\cal P}_τ\propto k^3$ and ${\cal B}^{\rm eq}_τ\propto k^6$. The eternal-background thresholds instead control the duration dependence of the moment coefficients and the crossover into an intermediate tail-sensitive regime, in agreement with our numerical calculations. We further show that temporal localization of the nucleation history provides a smooth regulator of the ancient-bubble tail and restores the same analytic infrared limits. These results establish a general first-arrival framework for completion-time fluctuations and clarify how de Sitter expansion can generate distinct power-spectrum and bispectrum infrared hierarchies relevant to curvature perturbations and non-Gaussianity.
