轻粒子尖锐引力产生的普适类
Universality classes of sharp gravitational production of light particles
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中文总结 AI 辅助
本文对尖锐转变中轻粒子的引力产生进行分类，发现标度因子的正则性决定增强类型：$C^0$类呈二次增强，$C^1$类呈对数增强，$C^2$及以上无增强。
中文摘要 AI 辅助
我们建立了在连接标度因子不同渐近形式的尖锐转变过程中轻粒子引力产生的分类。一族具有转变持续时间$\Delta\eta$的光滑标度因子，其特征是在尖锐转变极限$\Delta\eta\to 0$下的正则性，导致三个定性不同的普适类：$C^0$、$C^1$和$C^2$或更光滑。我们发现$C^0$类表现出产生粒子能量密度的二次增强，$\rho\propto\Delta\eta^{-2}$，而$C^1$类表现出对数增强，$\rho\propto\ln(1/\Delta\eta)$。对于$C^2$或更光滑类，不发生尖锐转变增强。使用一个特定的$C^\infty$标度因子模型，我们解析地推导了能量密度，并通过数值求解模方程确认了预测的二次标度及其系数。这些结果将标度因子在尖锐极限下的正则性确定为控制尖锐转变增强的关键属性。
英文摘要
We establish a classification of the gravitational production of light particles across sharp transitions connecting different asymptotic forms of the scale factor. A family of smooth scale factors with a transition duration $Δη$ is characterized by its regularity in the sharp-transition limit $Δη\to 0$, leading to three qualitatively different universality classes: $C^0$, $C^1$, and $C^2$-or-smoother. We find that the $C^0$ class exhibits a quadratic enhancement in the energy density of produced particles, $ρ\proptoΔη^{-2}$, while the $C^1$ class shows a logarithmic enhancement, $ρ\propto\ln(1/Δη)$. No sharp-transition enhancement occurs for the $C^2$-or-smoother class. Using a specific $C^\infty$ model of the scale factor, we derive the energy density analytically and confirm both the predicted quadratic scaling and its coefficient by numerically solving the mode equation. These results identify the regularity of the scale factor in the sharp limit as the key property controlling the sharp-transition enhancement.
发表机构
- Nagoya University（名古屋大学）
- Academia Sinica Institute of Astronomy and Astrophysics (ASIAA)（中央研究院天文及天文物理研究所）
- Kobayashi Maskawa Institute, Nagoya University（名古屋大学小川-益川研究所）
- Department of Physics, Nagoya University（名古屋大学物理学系）
- Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo（东京大学理化学研究所 Kavli宇宙物质起源研究前沿中心）
机构由 AI 辅助整理，请以论文原文为准。
