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

宇宙大尺度结构：非线性动力学和非高斯统计

• 批准号: 2441314
• 金额: --
• 依托单位: Newcastle University
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2441314
• 关键词: cosmic; large; scale; structure; non

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.

主题：数学科学和物理科学研究领域：数学物理、非线性系统----------------------------------------------------理解我们在宇宙中的位置、宇宙的起源和最终命运是我们所问的一些最基本的问题。在上一个世纪，我们已经开始回答这些问题，而不仅仅是哲学思考，而是通过经验和科学的调查。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不是静态的，实际上是在膨胀的。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。近十年来，大规模的实验在不久的将来有望实现，这使我们坚定地进入了精确宇宙学的时代。在这个时代，我们可以对宇宙的内容和动力学做出描述，相关误差在百分之一或以下。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，这需要宇宙初始条件的精确知识，但我们可以对可观测量的统计数据（如星系位置）进行陈述。迄今为止，宇宙学中的大多数强约束来自测量宇宙微波背景（CMB）的统计数据，即大爆炸后37万年的光。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多几个数量级的信息。从这个宇宙结构中获取有关宇宙学和基础物理学的信息是我项目的重点。我的研究集中在大尺度结构的两个特殊方面。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。由于暗物质的数量超过“正常”物质的4倍，它是形成大型结构的驱动力。然而，暗物质动力学的标准处理方法仅在一定长度尺度以上有效，低于该长度尺度，运动方程变得非线性。理解这种非线性状态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，也是大尺度结构的骨架。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（包括涡旋和湍流）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，并寻找特定暗物质候选者的特征签名。第二个方面是开发新的统计技术，可用于提取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数据，强大的数学原理（来自大偏差理论）确保对动态的主要贡献也具有相同的对称性。使用一些物理成分，我们可以从第一原理预测这些统计数据-包括它们对描述引力、中微子质量或早期宇宙的基本参数的依赖性。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，这些信息在标准宇宙学分析技术中丢失，提供了强大的补充调查路线。