The dark Universe in the light of its morphology

在过去的十年里，星系红移观测在测量星系在更大尺度上的分布结构方面取得了极大的成功。大量正在进行和计划中的光谱测量，如BOSS、EBOSS、DESI、4MOST和欧几里德，将最终提供可观测宇宙相当一部分的三维地图。该项目的目的是开发基于Minkowski泛函的分析工具，并充分利用这张星系位置地图中包含的丰富信息。在精密宇宙学的时代，我们将获得的信息的补充将对于揭示支配宇宙命运的暗成分的物理起源至关重要。我们使用的四个Minkowski泛函独特地量化了任何扩展的天体的形状。第一个泛函给出了物体的体积，第二个给出了它的表面积，第三个给出了它的积分平均曲率，最后一个给出了它的欧拉特性。与将一组点转换为光滑物体的处方一起，泛函描述了我们在星系分布中看到的复杂形状，如细丝和空洞。这种丰富的结构在星系调查中看到，并不完全被通常的分析所捕获，基于两点关联函数。后者仅衡量了结构的强弱程度如何提高了在给定距离内发现两个星系的可能性。使用Minkowski泛函的主要优点是，除了标准的两点性质外，它们还通过解析关系包含来自所有高阶关联的信息。我们将使用Minkowski泛函中的这些额外信息来更精确地测试宇宙模型。为了实现这一目标，我们首先分析我们可以用我们开发的方法测试最好的宇宙学参数。特别是，我们将尝试确定一种标准尺子，用于精确测量宇宙距离，因此也就是暗能量。我们还将尝试使用Minkowski泛函来改进对暗物质和星系星团差异的分析。在下一步，我们将测试将宇宙学模型与观测联系起来的常用建模假设。在第三步中，我们将应用第一步中开发的方法和第二步中确定的最佳建模假设来执行宇宙模型的数值测试。为此，我们将用我们的数值代码分析当前和未来的星系红移调查。最后，Minkowski泛函被活跃地应用于从固体物理到生物物理的不同科学领域，甚至被用于医学应用。因此，我们将在这个项目中开发的理论方法和高效代码的影响可能超出宇宙学应用的范围。

Over the last decade, galaxy redshift surveys have been extremely successful in measuring the structure of the galaxy distribution on ever larger scales. The large number of ongoing and planned spectroscopic surveys like BOSS, eBOSS, DESI, 4Most and Euclid will finally deliver a three dimensional map of a significant fraction of the observable universe.The aim of this project is to develop analysis tools that are based on Minkowski Functionals and fully exploit the wealth of information contained in this map of galaxy positions. In the era of precision cosmology, the supplement of information that we will access will be crucial to uncover the physical origin of the dark components that govern the fate of the universe.The four Minkowski Functionals we use uniquely quantify the shape of any extended body. The first functional gives the volume of the body, the second its surface area, the third its integrated mean curvature and the last its Euler characteristic. Together with a prescription that converts a set of points into a smooth body, the functionals characterize the complex shapes that we see in the distribution of galaxies, such as filaments and voids.This rich structure seen in galaxy surveys is not entirely captured by the usual analysis, based on the two-point correlation function. This latter only measures how strongly structure enhances the probability of finding two galaxies at a given distance from one another. The key advantage of using Minkowski Functionals is that, in addition to the standard two-point properties, they include information from all higher-order correlations, through an analytic relation. We will use this extra information in Minkowski Functionals to test cosmological models more precisely.To achieve this goal, we first analyse which cosmological parameters we can test the best with the method we will develop. In particular we will try to identify a standard ruler for a precise measurement of cosmic distances, and thus of dark energy. We will also attempt to use Minkowski Functionals to improve the analysis of the difference of clustering of dark matter and galaxies. In a next step, we will test commonly employed modelling assumptions which connect cosmological models to observations. In the third step, we will apply the method developed in the first step with the best modelling assumptions identified in the second step to perform a numerical test of cosmological models. To do so we will analyze current and future galaxy redshift surveys with our numerical codes.Finally, Minkowski Functionals are actively employed in different areas of Science from solid state physics, to biophysics and are even used in medical applications. Consequently, the impact of the theoretical methods and efficient codes we will develop during this project can go beyond cosmological applications.