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arXiv 2403.01416astro-ph.COgr-qchep-ph
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超慢滚暴胀中原始曲率扰动演化的解析近似

An analytical approximation of the evolution of the primordial curvature perturbation in the ultraslow-roll inflation

Ji-Xiang Zhao, Nan Li

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发表信息：
published in Eur. Phys. J. C 84, 222 (2024)
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AI总结：

针对超慢滚暴胀中原始曲率扰动演化问题，提出解析近似方法，揭示其复平面演化特征，解释功率谱形态并证明最小值非零，助力原初黑洞与引力波模型构建。

摘要：

若暴胀子势存在平台区，宇宙暴胀可进入超慢滚（USR）阶段。在此阶段，原始曲率扰动${\mathcal R}_k$及其功率谱${\mathcal P}_{\mathcal R}$在小尺度上会得到显著增强。本文提出一种解析近似方法，用于系统研究USR暴胀中${\mathcal R}_k$的演化。我们首先分别讨论了亚视界和超视界尺度下，${\mathcal R}_k$的模、幅角及其对时间的导数${\mathcal R}_{k,N}$的渐近解，发现所有这些解都具有简单的指数形式。随后，我们依次研究了五种典型尺度下的${\mathcal R}_k$。我们的解析近似预言，${\mathcal R}_k$首先在复平面上绕原点旋转；但若它在USR阶段开始前后穿越视界，则会随后出现朝向或远离原点的线性演化。这一行为自然解释了${\mathcal P}_{\mathcal R}$从陡降到峰值的形状，且与数值结果完美吻合。此外，本文严格证明了${\mathcal P}_{\mathcal R}$的最小值非零。我们的解析近似将有助于原初黑洞和引力波物理领域的模型构建。

英文摘要：

Cosmic inflation can enter an ultraslow-roll (USR) stage, if there is a plateau on the inflaton potential. During this stage, the primordial curvature perturbation ${\mathcal R}_k$ and its power spectrum ${\mathcal P}_{\mathcal R}$ can be remarkably enhanced on small scales. In this work, an analytical approximation is provided to systematically study the evolution of ${\mathcal R}_k$ in the USR inflation. We first discuss the asymptotic solutions of the moduli and arguments of ${\mathcal R}_k$ and its time derivative ${\mathcal R}_{k,N}$ on the sub- and super-horizon scales separately and find that all these solutions have simple exponential forms. Then, ${\mathcal R}_k$ on five typical scales are investigated in order. Our analytical approximation predicts that ${\mathcal R}_k$ first revolves around the origin in the complex plane, but if it crosses the horizon around the start of the USR stage, there appears a subsequent linear evolution towards or away from the origin. This behavior naturally explains the shape of ${\mathcal P}_{\mathcal R}$ from the sharp dip to the peak and matches the numerical results perfectly. Moreover, the minimum of ${\mathcal P}_{\mathcal R}$ is exactly proved to be nonvanishing. Our analytical approximation will help the model building in primordial black hole and gravitational wave physics.

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