Stochastic Bubble Completion in de Sitter Space: Power Spectrum, Bispectrum, and Infrared Moment Hierarchies
Abstract
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 Pτ∝ k3 and cal Beqτ∝ k6. 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.
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BibTeX
@misc{kim2026stochastic,
title = {{Stochastic Bubble Completion in de Sitter Space: Power Spectrum, Bispectrum, and Infrared Moment Hierarchies}},
author = {Hyukjung Kim and Alp Kagan Ozmen and Heeseung Zoe},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07880},
eprint = {2610.07880},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07880},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stochastic Bubble Completion in de Sitter Space: Power Spectrum, Bispectrum, and Infrared Moment Hierarchies
AU - Hyukjung Kim
AU - Alp Kagan Ozmen
AU - Heeseung Zoe
PY - 2026
DA - 2026/10/06
PB - arXiv
DO - 10.48550/arxiv.2610.07880
UR - https://arxiv.org/abs/2610.07880
AB - 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∝ k^3 and cal B^eq_τ∝ 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.
ER -