Kinetic Field Theory: Second-order perturbation theory

动场论：二阶微扰理论

• 批准号: 418152809
• 负责人: Professor Dr. Matthias Bartelmann
• 金额: --
• 依托单位: Institut für Theoretische Physik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2019
• 资助国家: 德国
• 起止时间: 2018-12-31 至 2020-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/418152809?language=en
• 关键词: Kinetic; Field; Theory; Second; order

Astoundingly successful as it is, the cosmological standard model leaves us with two difficult and fundamentally important puzzles, viz. the dark matter and the dark energy, whose origin, composition, and place in the framework of physics are enigmatic. Large cosmological surveys are being and are about to be undertaken with the major goals of mapping and quantifying the dark-matter distribution and finding out about a possible evolution of the dark-energy density with time. Precise cosmological inference from these surveys hinges on the depth and precision of our understanding of the late-time, non-linear evolution of cosmic structures. While numerical simulations have returned a wealth of impressive and important results, calculating higher-order statistical properties of large-scale cosmic structures at late times is still a forbiddingly time-consuming task.Recently, we have developed a novel analytic approach to non-linear cosmic structure formation, based on a non-equilibrium kinetic field theory (KFT). This theory has several important advantages compared to more conventional approaches. In particular, it operates on the microscopic degrees of freedom of classical particles in phase space. Since the Hamiltonian flow in phase space is bijective and diffeomorphic, the notorious shell-crossing problem is absent from our approach. In its present form, the theory is free of adjustable parameters. We have shown in earlier work that even first-order perturbation theory applied to KFT reproduces the non-linear power spectrum of cosmic density fluctuations very well to wave numbers of k ~ 10 h/Mpc at the present cosmic epoch. We could further show how the central mathematical object of KFT, its generating functional, can be fully factorized into terms of a standard form.Based on this factorization, a diagrammatic approach to perturbation theory developed therefrom, and a first version of a symbolic computer code for constructing these diagrams, we propose here to calculate the second-order perturbation terms for the non-linear power spectrum of cosmic density fluctuations. Main challenges will be the reliable and fast numerical integration of the generic expressions appearing in the factorization of the generating functional, and the calculation of the one- and two-loop integrals appearing in the perturbation series. The essential goals of the proposed research are to finalize and test our symbolic computer code for perturbation diagrams, to supply it with a code for numerical integration of perturbation terms, and to evaluate, analyze and compare the contributions of these terms to the non-linearly evolved cosmic power spectrum. Based on the quality of the first-order perturbation theory in KFT, we are confident that we can analytically calculate accurate non-linear power spectra reaching wave numbers of k ~ 20-50 h/Mpc at the present epoch.

尽管宇宙学标准模型取得了惊人的成功，但它给我们留下了两个困难而又至关重要的难题，即暗物质和暗能量，它们的起源、组成和在物理学框架中的位置都是谜。大型宇宙学调查正在进行，并即将进行的主要目标是映射和量化的暗物质分布，并找出一个可能的演化的暗能量密度随时间的推移。从这些调查中精确的宇宙学推断取决于我们对宇宙结构晚期非线性演化的理解的深度和精度。虽然数值模拟已经返回了丰富的令人印象深刻的和重要的结果，计算高阶统计性质的大尺度宇宙结构在后期的时间仍然是一个令人生畏的耗时task.Recently，我们已经开发了一种新的分析方法，非线性宇宙结构的形成，基于非平衡动力学场理论（KFT）。与更传统的方法相比，该理论具有几个重要的优点。特别地，它作用于相空间中经典粒子的微观自由度。由于相空间中的哈密顿流是双射的，并且是双纯的，所以我们的方法中没有臭名昭著的壳交叉问题。在其目前的形式，理论是自由的可调参数。我们在早期的工作中已经表明，即使是一阶微扰理论应用于KFT再现宇宙密度波动的非线性功率谱非常好的波数k ~ 10 h/Mpc在目前的宇宙时代。我们可以进一步说明如何中心的数学对象KFT，它的生成功能，可以完全分解成一个标准形式的条款。基于这种分解，从发展的微扰理论的图解方法，和第一个版本的符号计算机代码，用于构建这些图，我们建议在这里计算的二阶微扰项的非线性功率谱的宇宙密度波动。主要的挑战将是可靠和快速的数值积分的通用表达式出现在因式分解的生成功能，和计算的一个和两个循环的积分出现在扰动系列。拟议中的研究的基本目标是完成和测试我们的符号计算机代码的扰动图，提供一个代码的数值积分的扰动项，并评估，分析和比较这些条款的非线性演变的宇宙功率谱的贡献。基于KFT的一阶微扰理论的性质，我们相信，在目前的时代，我们可以解析地计算出波数达到k ~ 20-50 h/Mpc的精确非线性功率谱。