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

IF 3 3区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Annals of Physics Pub Date : 2024-10-09 DOI:10.1016/j.aop.2024.169824

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引用次数: 0

Abstract

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.

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预热过程中的自共振α-吸引器模型的情况

在本文中，我们首次获得了希尔型微分方程的一类新解，它们出现在宇宙膨胀的预热自共振阶段。我们特别研究了对称和非对称标量场势，它们来自早期宇宙学中所谓的α-吸引子模型。通过对势能进行数列展开并运用微扰技术，我们将捕捉这些模型中曲率扰动动态的穆哈诺夫-萨崎方程重新表述为希尔方程。最后一个方程包括了文献中从未解决的高阶项。即来自标量场势的三次方和四次方贡献的项。然后，我们推导出穆哈诺夫-萨崎变量的 Floquet 指数表达式。我们将分析结果与数值计算结果进行了比较，结果表明两者吻合得很好，从而使这种方法在原始黑洞和标量诱发引力波方面的理论预测和新的观测应用变得非常有价值。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annals of Physics 物理-物理：综合

CiteScore

5.30

自引率

3.30%

发文量

211

审稿时长

47 days

期刊介绍： Annals of Physics presents original work in all areas of basic theoretic physics research. Ideas are developed and fully explored, and thorough treatment is given to first principles and ultimate applications. Annals of Physics emphasizes clarity and intelligibility in the articles it publishes, thus making them as accessible as possible. Readers familiar with recent developments in the field are provided with sufficient detail and background to follow the arguments and understand their significance. The Editors of the journal cover all fields of theoretical physics. Articles published in the journal are typically longer than 20 pages.