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arXiv 2406.04017hep-thgr-qcmath-phmath.MP
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预热期间的自共振:$α$-吸引子模型的情形

Self-resonance during preheating: The case of $α$-attractor models

Daniel del-Corral

AI总结:

本文首次针对膨胀宇宙预热自共振阶段的Hill型方程提出新解,通过级数展开和微扰技术将$α$-吸引子模型中的Mukhanov-Sasaki方程转化为含高阶项的Hill方程,推导了Floquet指数,解析与数值结果一致,可用于原初黑洞和标量诱导引力波的观测预测。

摘要:

在本文中,我们首次针对Hill型微分方程获得了一类新解,该方程出现于膨胀宇宙的预热自共振阶段。特别地,我们研究了源自早期宇宙宇宙学中所谓$α$-吸引子模型的对称与非对称标量场势。通过对势进行级数展开并采用微扰技术,我们将描述这些模型中曲率扰动动力学的Mukhanov-Sasaki方程重新表述为Hill方程。后者包含了文献中从未被求解过的高阶项,即源自标量场势的三次和四次贡献项。接着,我们推导了Mukhanov-Sasaki变量的Floquet指数的表达式。随后,我们将解析结果与数值计算进行了比较,显示出良好的一致性,从而使该方法在获取理论预测方面具有重要价值,并在原初黑洞和标量诱导引力波背景下具有新的观测应用。

英文摘要:

In this paper, for the first time, we obtain a new class of solutions for the Hill-type differential equations, which emerge in the preheating self-resonance phase of the expanding Universe. We study, in particular, the class of symmetric and asymmetric scalar field potentials coming from the so-called $α$-attractor models of the early Universe cosmology. By making a series expansion of the potential and employing perturbative techniques we reformulate the Mukhanov-Sasaki equation, which captures the dynamics of the curvature perturbation in these models, into a Hill equation. This last includes higher-order terms that were never solved in the literature. Namely, those coming from the cubic and quartic contributions of the scalar field potential. Then, we derive the expressions for the Floquet exponents of the Mukhanov-Sasaki variable. Our analytical results are then compared with numerical computations, showing a good agreement and thus making this method valuable for obtaining theoretical predictions with new observational applications in the contexts of Primordial Black Holes and Scalar-Induced Gravitational Waves.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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