Cosmological simulations of large scale structure and general relativity

当前的标准宇宙学模型LCDM假设暗物质是冷物质，暗能量是一个宇宙常数λ，它基于以下三个主要因素：1）宇宙在最大尺度上是各向同性的，均匀的，因此很好地描述了Friedmann-Lemaitre-Robertson-Walker（FLRW）度规：2）大尺度结构可以用线性和非线性微扰方法模拟; 3）完全非线性结构的形成可以用牛顿N体模拟来描述。这个项目将解决最后一个假设有多好的问题。现代引力理论毕竟是广义相对论。随着最先进的宇宙学观测达到1%或更高的精度，并且在不久的将来甚至会有更大的改进，研究当前理论预测的准确性是非常及时的。现在有公开可用的牛顿N体代码，以及包含广义相对论修正的N体代码，可以用来模拟宇宙学中的大尺度结构。然而，这些编码包括一些相对论修正是否能捕捉到所有重要的效应还远未清楚。另一方面，我们最近首次成功地将数值相对论代码（i.e.codes）应用于宇宙学，尽管是在一个非常简化的设置中，并且使用了物质的流体描述，而不是N体代码的粒子描述。这个博士项目将建立在这些第一个开创性的工作，以进一步发展一个完全相对论的方法来研究大尺度结构。一个重要的目标是建立如何准确的牛顿和“GR校正”代码;另一个是测试各种广义相对论近似用于modelstructure形成在轻度非线性政权;这些问题可以通过使用现有的数值相对论代码作为基准来解决。另一个有待解决的问题是如何在非线性演化中准确地应用微扰论中的相对论性初始条件。有许多物理问题需要全面研究，从第一个宇宙学物体的坍缩到大空洞的形成，再到非线性结构的形成如何影响宇宙学中的光传播，最终影响观测。

The current standard model of cosmology, LCDM, assumes Cold Dark Matter and a cosmologicalconstant Lambda as Dark Energy, and is based on three main ingredients:1) the Universe is isotropic and homogeneous on the largest scales and thus well described theFriedmann-Lemaitre-Robertson-Walker (FLRW) metric;2) large-scale structure can be modelled by perturbative methods, linear and non-linear;3) fully nonlinear structure formation can be described by Newtonian N-body simulations.This project will address the question of how good this last assumption is. The modern theory ofgravity is, after all, General Relativity. With state-of-the-art cosmological observations reaching aprecision of 1% or better and even more improvement expected in the near future, it is extremelytimely to investigate how accurate the current theoretical predictions are.There are now publicly available Newtonian N-body codes, as well as N-body codes that includecorrections from General Relativity, that can be used to model large-scale structure in cosmology.However, it is far from clear that these codes including some relativistic corrections capture all theimportant effects. On the other hand, we recently successfully applied numerical relativity codes (i.e.codes that are fully relativistic) in cosmology for the first time, albeit in a very simplified setting andusing a fluid description of matter, rather than the particle description of N-body codes. This PhDproject will build on these first pioneering works to further develop a fully relativistic approach to thestudy of large-scale structure. One important goal is to establish how accurate Newtonian and "GRcorrected" codes are; another is to test various general-relativist approximations used to modelstructure formation in the mildly-non-linear regime; these issues can be addressed by using existingnumerical relativity codes as benchmark. Another open problem to address is that of accuratelyimplementing relativistic initial conditions derived from perturbation theory into the nonlinear evolution.There is a number of physical questions that need investigation in full GR, from the collapse of the firstcosmological objects to the formation of large voids, to how the formation of nonlinear structuresaffects light propagation in cosmology, ultimately affecting observations.