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arXiv 2507.08075astro-ph.COhep-phmath-phmath.MP
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Hill方程参数的涨落及其在宇宙重加热中的应用

Fluctuations in Hill's equation parameters and application to cosmic reheating

Leia Barrowes, Fred C. Adams, Anthony M. Bloch, Scott Watson

AI总结:

本文研究了Hill方程参数的随机涨落对宇宙重加热期间粒子产生的影响,发现随机噪声能显著改变共振稳定带并大幅增强粒子产生,从而在广阔参数空间内提升重加热效率。

摘要:

宇宙暴胀为解释我们宇宙的若干观测特征提供了一个令人信服的框架,但其可行性取决于一个高效的重加热阶段,该阶段将暴胀子的能量转化为Standard Model粒子。这种转化通常通过非微扰机制(如参数共振)进行,该机制由Hill方程描述。在这项工作中,我们研究了Hill方程参数的随机涨落如何影响重加热期间的粒子产生。我们表明,这种涨落可能源于与轻标量场的耦合,并且可以显著改变共振结构中的稳定带,从而增强涨落的增长并拓宽高效能量转移的区域。使用随机矩阵理论和随机微分方程,我们将粒子增长率分解为确定性分量和噪声诱导分量,并在解析和数值上证明,即使是适度的噪声也会在原本稳定的区域中导致大量粒子产生。这些结果表明,随机效应可以在广阔的参数空间范围内稳健地增强重加热的效率,对早期宇宙学、涉及多个标量场的UV完备化以及宇宙学模问题的解决具有重要意义。

英文摘要:

Cosmic inflation provides a compelling framework for explaining several observed features of our Universe, but its viability depends on an efficient reheating phase that converts the inflaton's energy into Standard Model particles. This conversion often proceeds through non-perturbative mechanisms such as parametric resonance, which is described by Hill's equation. In this work, we investigate how stochastic fluctuations in the parameters of Hill's equation can influence particle production during reheating. We show that such fluctuations can arise from couplings to light scalar fields, and can significantly alter the stability bands in the resonance structure, thereby enhancing the growth of fluctuations and broadening the region of efficient energy transfer. Using random matrix theory and stochastic differential equations, we decompose the particle growth rate into deterministic and noise-induced components and demonstrate analytically and numerically that even modest noise leads to substantial particle production in otherwise stable regimes. These results suggest that stochastic effects can robustly enhance the efficacy of reheating across a wide swath of parameter space, with implications for early Universe cosmology, UV completions involving multiple scalar fields, and the resolution of the cosmological moduli problem.

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