The cosmic large scale structure: non-linear dynamics and non-Gaussian statistics

主题：数学科学和物理科学研究领域：数学物理，非线性systems----------------------------------------------------Cosmology，在最大长度和时间尺度上研究宇宙，几千年来一直是人类问题的核心。理解我们在宇宙中的位置，宇宙的起源，以及宇宙的最终命运，是一些最基本的问题。在上个世纪，我们已经开始不再简单地用哲学思辨来回答这些问题，而是通过经验和科学的探索。这种宇宙学的科学方法真正开始于20世纪20年代，当时对遥远星系的测量表明，宇宙并不是静态的，实际上正在膨胀。1998年，对遥远的垂死恒星的测量表明，宇宙不仅在膨胀，而且在加速。过去的十年，以及在不久的将来进行大规模实验的前景，将我们坚定地带入了精密宇宙学的时代，在这个时代，我们可以对宇宙的内容和动力学做出声明，相关误差在百分比水平或更低。宇宙学的预测本质上是统计学的。例如，我们不能预测在天空中的任何给定位置是否会有一个星系，这需要对宇宙的初始条件有准确的了解，但我们可以就诸如星系位置等可观测数量的统计数据发表声明。到目前为止，宇宙学中的大多数强约束来自于测量宇宙微波背景(CMB)的统计数据，CMB是大爆炸后37万年的光线。虽然这为现代宇宙学提供了一个强有力的起点，但宇宙的大尺度结构-暗物质和星系的网状网络-可能比CMB拥有更多数量级的信息。从这个宇宙结构中获取有关宇宙学和基础物理的信息是我的项目的重点。我的研究集中在大尺度结构的两个特定方面。我的第一个项目是更好地理解暗物质的非线性引力动力学。由于暗物质的数量是正常物质的4：1，它是形成大结构的驱动力。然而，暗物质动力学的标准处理方法只有在一定的长度尺度上才有效，低于这个长度尺度，运动方程就变成了非线性的。了解这种非线性机制对于理解被称为暗物质晕的束缚结构至关重要，暗物质晕是星系的宿主，并奠定了大尺度结构的骨架。我的项目将专注于描述引力暗物质动力学的新技术，特别是使用量子经典对应及其与量子流体现象(包括涡度和湍流)的联系。目标是开发新的分析和计算工具来解决暗物质进入这种非线性区域的时间演化，并寻找特定候选暗物质的特征特征。第二个方面是开发新的统计技术，可以用来提取对当前宇宙学参数的约束，并研究新的基础物理。这些技术基于选择具有特定对称性的统计量，对于这种对称性，强大的数学原理(来自大偏差理论)确保了对动力学的主要贡献也具有这种对称性。使用一些物理成分，我们可以根据第一原理预测这些统计数据--包括它们对描述重力、中微子质量或早期宇宙的基本参数的依赖。这些技术可以从物质分布的非高斯统计中提取额外的信息，这些信息在标准的宇宙分析技术中丢失，提供了强大和补充的研究路线。

Themes: mathematical sciences and physical sciencesResearch areas: mathematical physics, non-linear systems----------------------------------------------------Cosmology, the study of the universe on the largest length and time scales, has been at the heart of human questions for millenia. Understanding our place in, the origins of, and the ultimate fate of the universe are some of the most fundamental questions asked. In the last century, we have begun to answer these questions not simply with philosophical speculation, but through empirical and scientific enquiry. This scientific approach to cosmology began in earnest in the 1920s when measurements of distant galaxies indicated that the universe was not static, and was in fact expanding. In 1998, measurements of distant dying stars indicated that the universe is not only expanding, but accelerating. The last decade, and the promise of large scale near future experiments puts us firmly into the era of precision cosmology, where we can make statements about the contents and dynamics of the universe with associated errors at or below the percent level.Predictions in cosmology are by nature statistical. For example, we cannot predict if there will be a galaxy at any given position in the sky, which would require exact knowledge of the initial conditions of the universe, but we can make statements about the statistics of observable quantities such as galaxy positions. To date, most of the strong constraints in cosmology come from measuring the statistics of the cosmic microwave background (CMB), light from 370,000 years after the big bang. While this has provided a strong starting place for modern cosmology, the large scale structure of the universe - a weblike network of dark matter and galaxies - potentially holds orders of magnitude more information than the CMB. Accessing information about cosmology and fundamental physics from this cosmic structure is the focus of my project.My research focuses on two particular aspects of large scale structure. The first of my project is better understanding the nonlinear gravitational dynamics of dark matter. As the dark matter outnumbers "normal" matter 4 to 1, it is the driving force in the formation of large structures. However, standard treatments of dark matter dynamics are only valid above a certain length scale, below which the equations of motion become nonlinear. Understanding this nonlinear regime is crucial for understanding bound structures called dark matter halos, which host galaxies and set the skeleton of the large scale structure. My project will focus on novel techniques to describe gravitational dark matter dynamics, in particular using the quantum-classical correspondence and its links to quantum fluid phenomena (including vorticity and turbulence). The goal is to develop new analytical and computational tools to solve the time-evolution of dark matter into this nonlinear regime and to hunt for the characteristic signature of particular dark matter candidates.The second aspect is developing novel statistical techniques that can be used to extract constraints on current cosmological parameters and investigate new fundamental physics. These techniques are based on choosing statistics with particular symmetries, for which powerful mathematical principles (from large deviation theory) ensure that the dominant contribution to the dynamics also has this same symmetry. Using a few physical ingredients we can predict these statistics from first principles - including their dependence on fundamental parameters describing gravity, neutrino masses, or the early universe. These techniques can extract additional information from the non-Gaussian statistics of the matter distribution that are lost in standard cosmological analysis techniques, providing powerful and complementary routes of investigation.