Interpretation of relativistic effects and corrections within cosmological structure formation

根据宇宙学的标准模型，大尺度结构（即，星系团）的形成在很大程度上是引力不稳定的结果。通过分析和数值方法研究引力演化，我们可以验证引力理论，但我们也能够揭示我们宇宙的能量组成。后者也意味着理解尚未发现的暗物质和暗能量的神秘本质。到目前为止，所有测量到的宇宙尺度（1 Mpc - 100 Mpc）的效应都只限于广义相对论中的首阶。抛开纯粹的相对论效应（例如，引力透镜效应），相对论修正通常进入超过首阶，即，这样的修正相对于牛顿体部分是小的。目前和即将进行的大规模调查（如SDSS或欧空局的欧几里得卫星）将以前所未有的精度解决大规模结构，并将宇宙学模型中的不确定性降低到百分之一的水平。因此，将来自广义相对论的效应和修正限制到足够的精度是至关重要的。确定宇宙结构形成中的相对论效应是拟议项目的目标之一。最重要的是，这个项目的目的是集中在相对论结构形成中观察者的基本作用。我们将研究相对论效应如何影响观测的解释，这在广义相对论中是一个重要的问题。当我们解释观测数据时，这一点变得越来越重要，特别是考虑到宇宙学已经成为一门精确的科学。此外，我的项目部分是将这些发现应用于数值模拟的相对论解释。这些模拟使用牛顿近似，因为完全相对论处理是不可行的。基本目标是提供牛顿模拟和广义相对论之间的直接联系，即，粒子的位置是否必须根据相对论约束进行更新/移位，和/或数值模拟中的网格单元的体积是否变形。这些（以及以下）考虑的关键分析技术是拉格朗日微扰理论，我在多年的研究中获得了这方面的专业知识。我还将继续我目前的努力，在这种数值模拟的初始条件中嵌入相对论修正。成功的考虑可以建立简单和计算速度快的准相对论模拟。

According to the standard model of cosmology the large-scale structure (i.e., clusters of galaxies) of the universe is largely the result of gravitational instability. By studying the gravitational evolution with analytical and numerical methods we can verify the theory of gravitation, but we are also able to shed light into the energy composition of our universe. The latter also means to understand the mysterious nature of the yet undiscovered dark matter and dark energy.So far all measured effects on cosmological scales (1 Mpc - 100 Mpc) are only constrained up to leading order within general relativity. Putting aside purely relativistic effects (e.g., the gravitational lensing), relativistic corrections usually enter beyond leading order, i.e., such corrections are small with respect to the Newtonian bulk part. Current and forthcoming large-scale surveys (such as SDSS or ESA's Euclid satellite) will resolve the large-scale structure to unprecedented accuracy, and reduce uncertainties within the cosmological model to the per cent level. Thus, it is crucial to constrain effects and corrections coming from general relativity to sufficient accuracy.Identifying relativistic effects within cosmological structure formation is one of the objectives in the proposed project. Most importantly, the aim of this project is to concentrate on the fundamental role of the observer in relativistic structure formation. We shall investigate how relativistic effects affect the interpretation of observations, which is a non-trivial issue in general relativity. This becomes increasingly important when we interpret survey data-especially considering that cosmology has moved into being a precision science.Additionally, my part of the project is to apply the findings to a relativistic interpretation of numerical simulations. These simulations use the Newtonian approximation because a fully relativistic treatment is not feasible. The essential objective is to deliver a direct connection between Newtonian simulations and general relativity, i.e., whether the particle's positions have to be updated/displaced according to the relativistic constraints, and/or whether the volume of the grid cells in the numerical simulation is deformed. The key analytic technique for these (and the following) considerations is the Lagrangian perturbation theory, in which I have gained expertise in my years of research.I will also proceed with my current efforts in embedding relativistic corrections in terms of the initial conditions of such numerical simulations. Successful considerations could then establish simple and computationally fast quasi-relativistic simulations.