Cosmological simulations of large scale structure and general relativity

目前的宇宙学标准模型LCDM假定冷暗物质和宇宙常数Lambda为暗能量，并基于三个主要成分：1)宇宙在最大尺度上是各向同性和均匀的，因此很好地描述了Friedmann-Lemaitre-Robertson-Walker(FLRW)度规；2)大尺度结构可以用微扰方法建模，线性和非线性；3)完全非线性的结构形成可以用牛顿N体模拟来描述。本项目将解决最后一个假设有多好的问题。毕竟，现代引力理论是广义相对论。随着最先进的宇宙学观测达到1%或更高的精度，并有望在不久的将来得到更大的改善，现在是研究当前理论预测的精确度的极及时的时候。现在有公开可用的牛顿N体代码，以及包括广义相对论修正的N体代码，可以用来模拟宇宙学中的大尺度结构。然而，目前还不清楚这些代码包括一些相对论修正是否涵盖了所有重要的影响。另一方面，我们最近首次成功地将数值相对论代码(即完全相对论的代码)应用于宇宙学，尽管是在非常简化的环境中，并且使用了物质的流体描述，而不是N体代码的粒子描述。这个博士项目将在这些开创性工作的基础上，进一步发展一种完全相对论的方法来研究大规模结构。一个重要的目标是确定牛顿编码和“GR校正”编码的精确度；另一个目标是测试用于在温和非线性区域模拟结构形成的各种广义相对主义近似；这些问题可以通过使用现有的数值相对论编码作为基准来解决。另一个有待解决的问题是如何准确地将从微扰理论得到的相对论初始条件应用到非线性演化中。从第一个宇宙学物体的坍塌到大空洞的形成，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，有许多物理问题需要全面研究。

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.