Cosmic Structures: From Cosmology to Interstellar Medium

宇宙学家现在对我们宇宙中结构形成的整体图景充满信心。我们宇宙的复杂性来自早期宇宙迅速膨胀时物质的微小量子涨落。后来，在重力的作用下，不均匀物质成长为恒星、星系，并在大尺度上形成了星系网，在宇宙微波背景(CMB)上留下了印记。但基本的问题也被提出了：我们如何才能窥探大爆炸前早期通胀阶段的细节？什么是‘暗物质’和‘暗能量’，成功的模型必须假设在宇宙中占主导地位？3D银河系星表中观察到的丝状宇宙星系网是如何形成的，它是如何组织起来的？我们对宇宙的许多了解，都是从对物质的大尺度分布的统计分析中学到的，并将CMB的天空图视为随机场。我提议从事的这些领域的几何分析有可能回答这些新的中心问题。关键是寻找几何统计数据与正常的、即所谓的“高斯”行为的偏差。我提出了对这种非高斯主义的高级理论描述。应用到中巴身上，它可能会告诉我们，通胀模型是否可以区分，甚至可以证明是错误的。应用到今天的结构演化，它可能会帮助我们确定什么是难以捉摸的“暗能量”。

Cosmologists are now confident in the overall picture of structure formation in our Universe. The complexity of our Universe came from tiny quantum fluctuations of matter at an early era when the Universe was rapidly inflating. Inhomogeneities later grew under the force of gravity into stars, galaxies and, at large scales, the galactic Web, leaving an imprint on the Cosmic Microwave Background (CMB) along the way. But fundamental questions have also been raised: How can we peek into details of that early inflationary stage before the Big Bang? What are the 'dark matter' and 'dark energy' that successful models have to assume to dominate in the Universe? How did the filamentary Cosmic Web of galaxies observed in 3D galactic catalogues come into being and is it organized? Much of what we know about the Universe, we learned from statistical analysis of the large scale distribution of matter and CMB sky-maps treated as random field. Geometrical analysis of such fields that I propose to pursue has the potential to answer these new central questions. The key is to look for deviations in geometrical statistics from the normal, so-called "Gaussian", behaviour. I have developed advanced theoretical description of such non-Gaussianity. Applied to CMB, it may tell us whether inflationary models can be distinguished between, or even disproved. Applied to present day evolution of the structure, it may help us to determine what the elusive "dark energy" is.