Non-linear cosmic structure formation in the mean-field approximation

平均场近似中的非线性宇宙结构形成

• 批准号: 528166846
• 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
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/528166846?language=en
• 关键词: Non; linear; cosmic; structure; formation

Understanding the formation of non-linear cosmic structures is important not only because the analysis of current and upcoming data depends on it, but also because these structures in reality as well as in simulations reveal signs of universality whose origin is unclear. Recently, a new analytic approach to non-linear structure formation in classical particle systems in and out of equilibrium has been developed, based on kinetic field theory (KFT). This approach avoids the shell-crossing problem of more conventional approaches by construction and thus allows to enter quite deeply into the non-linear regime even at low orders of perturbation theory. In addition, a mean-field approximation has been developed within KFT that reproduces non-linear power spectra of numerically simulated cosmic density fluctuations at the per-cent level in a wide range of wave numbers in the trans-linear and non-linear regimes. This mean-field approximation has so far been derived in a heuristic way. Motivated by its success, the present proposal aims at clarifying its foundations, placing it on a rigorous derivation, and extending it towards spectra of higher order, such as the bi- or trispectrum. The work programme foresees developing probability distributions for finding particles correlated with the mean density field in evolved ensembles of classical particles out of equilibrium under appropriately realistic approximations, averaging interaction terms in the generating functional of KFT with these probability distributions, and deriving power spectra, bispectra, and possibly trispectra. It further foresees studying how the Hubbard-Stratonovich transformation could be introduced into KFT in a cosmological context, and how this transformation could be used to further understand and develop the mean-field approximation to cosmic structure formation. This approach will also allow to extend studies of non-linear cosmic structures to non-standard cosmological models or theories of gravity.

理解非线性宇宙结构的形成是重要的，不仅因为对当前和即将到来的数据的分析依赖于它，而且因为这些结构在现实中以及在模拟中揭示了起源尚不清楚的普遍性的迹象。最近，一种新的分析方法，在经典粒子系统的非线性结构的形成和平衡的基础上，动力学场理论（KFT）已经开发。这种方法避免了壳交叉的问题，更传统的方法通过建设，从而允许进入相当深入的非线性制度，即使在低阶微扰理论。此外，平均场近似已开发内KFT再现非线性功率谱的数值模拟宇宙密度波动的百分之一级在广泛的波数范围内的trans-linear和非线性制度。到目前为止，这种平均场近似是以启发式的方式推导出来的。受其成功的动机，本建议的目的是澄清其基础，把它放在一个严格的推导，并将其扩展到更高的顺序，如双或三谱的光谱。该工作计划预计开发的概率分布找到粒子相关的平均密度场的经典粒子的演化合奏下适当的现实近似下的平衡，平均相互作用项的生成功能的KFT与这些概率分布，并推导出功率谱，bispectra，并可能trispectrum。它进一步预见研究如何在宇宙学背景下将Hubbard-Stratonovich变换引入KFT，以及如何使用这种变换来进一步理解和发展宇宙结构形成的平均场近似。这种方法还将允许将对非线性宇宙结构的研究扩展到非标准宇宙学模型或引力理论。