In earlier work, we have developed a Kinetic Field Theory (KFT) for cosmological structure formation and showed that the non-linear density-fluctuation power spectrum known from numerical simulations can be reproduced quite well even if particle interactions are taken into account to first order only. Besides approximating gravitational interactions, we had to truncate the initial correlation hierarchy of particle momenta at the second order. Here, we substantially simplify KFT. We show that its central object, the free generating functional, can be factorized, taking the full hierarchy of momentum correlations into account. The factors appearing in the generating functional, which we identify as non-linearly evolved density-fluctuation power spectra, have a universal form and can thus be tabulated for fast access in perturbation schemes.
In this paper, we focus on a complete evaluation of the free generating functional of KFT, not including particle interactions yet. This implies that the non-linearly evolved power spectra contain a damping term which reflects that structures are being wiped out at late times by free streaming. Once particle interactions will be taken into account, they will compensate this damping. If we suppress this damping in a way suggested by the fluctuation-dissipation relations of KFT, our results show that the complete hierarchy of initial momentum correlations is responsible for a large part of the characteristic non-linear deformation and the mode transport in the density-fluctuation power spectrum. Without any adjustable parameters, KFT accurately reproduces the scale at which non-linear evolution sets in.
Finally, we further develop perturbation theory based on the factorization of the generating functional and propose a diagrammatic scheme for the perturbation terms.
Analyzing the cosmic variance limit of remote dipole measurements of the cosmic microwave background using the large-scale kinetic Sunyaev Zel'dovich effect
Cosmic Structure Formation with Kinetic Field Theory
动力学场论（英语：Kinetic Field Theory，KFT）是一种统计学的场论，用于描述处于或不处于平衡状态的点状经典粒子系综。本文综述了它在宇宙结构形成中的应用。从理论的生成泛函的构建开始，我们详细描述了该理论需要如何适应以反映宇宙结构的扩展空间背景和均匀、各向同性、相关的初始条件。基于生成泛函，我们开发了三种主要的方法来非线性，晚时间宇宙结构，这取决于泰勒展开的相互作用算子，适当的平均程序的相互作用项，或重新定义的扰动项。我们展示了如何解析，无参数方程的非线性宇宙功率谱可以推导出来。我们解释了如何可以使用该理论来推导引力束缚结构的密度分布，并用它来推导宇宙速度密度的功率谱。我们进一步阐明了KFT与BBGKY层次结构的关系。然后，我们着手将动力学场论的流体，介绍了KFT的重新制定的宏观量，导致一个remmation计划，并使用它来描述气体和暗物质的混合物。我们讨论了如何KFT可以应用于研究宇宙结构的形成与修改后的引力理论。作为一个应用到非宇宙学粒子系综的例子，我们展示了从KFT得到的冷里德伯原子的空间关联函数的结果。
Cosmic voids and the kinetic analysis. V. Hubble tension, the cosmological constant and aperiodic filaments
Center for Cosmology and Astrophysics, Alikhanian National Laboratory（阿利哈尼扬国家实验室宇宙学与天体物理中心）；Yerevan State University（埃里温国立大学）；Sapienza Universita di Roma（罗马智慧大学）；Keldysh Institute of Applied Mathematics of RAS（俄罗斯科学院凯尔迪什应用数学研究所）
