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.

宇宙学标准模型令人惊讶地成功，这使我们遇到了两个困难且根本重要的难题，即。暗物质和暗能量，其起源，组成和物理框架中的位置是神秘的。大规模的宇宙学调查正在进行，即将以绘制和量化黑性分布的主要目标进行，并随着时间的推移发现黑暗能量密度的演变。这些调查的精确宇宙学推断取决于我们对宇宙结构的晚期，非线性演变的深度和精度。尽管数值模拟返回了许多令人印象深刻且重要的结果，但在后期计算大规模宇宙结构的高阶统计特性仍然是一项令人难以置信的耗时的任务。实际上，我们已经基于非平衡性Kinetic Field Theemens（Kft）开发了一种新型的分析方法，以针对非线性宇宙结构形成形成。与更传统的方法相比，该理论具有几个重要的优势。特别是，它在相空间中经典颗粒的显微镜自由度下运行。由于相位空间中的哈密顿流量是射精和差异性的，因此我们的方法中没有臭名昭著的壳横断问题。以目前的形式，该理论没有可调参数。我们在较早的工作中表明，即使是一阶扰动理论也适用于KFT，在当前宇宙时期，宇宙密度波动的非线性功率谱也非常好，以k〜10 h/mpc的波数。 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.主要挑战将是生成功能分解中出现的通用表达式的可靠，快速的数值集成，以及在扰动序列中出现的一环积分和两环积分的计算。拟议研究的基本目标是最终确定和测试我们的符号计算机代码的扰动图，为其提供扰动项的数值整合的代码，并评估，分析和比较这些术语对非线性演变的宇宙功率谱的贡献。基于KFT中一阶扰动理论的质量，我们有信心在当前时期分析计算准确的非线性功率谱，以达到k〜20-50 h/mpc的波数。