Cosmology and galaxy alignment with third-order weak lensing

We live in a Dark Universe. The accelerated expansion of our Universe is caused by the mysterious Dark Energy, while the equally mysterious Dark matter strongly influences the formation of structures inside it. One tool to shed light on these two ill-understood components is by using weak gravitational lensing- This technique involves measuring how the gravity of massive objects such as galaxies and galaxy clusters bends the path of light travelling through space. By analyzing this distortion of light, we can measure the distribution of matter in the Universe and study how it changes over time. The Euclid mission, set to launch this summer, aims to use weak gravitational lensing to study the cosmos in greater detail than ever before. However, the current methods for analyzing the data collected from these observations, so-called second-order statistics, cannot capture all the relevant information. To get the most out of the Euclid mission, scientists must develop new statistical tools to extract more information. One such tool is using so-called third-order statistics. In this study, we will develop new methods for analyzing third-order statistics of weak gravitational lensing. We investigate how these statistics can be used to better understand the Universe`s history and improve measurements of the shape of galaxy clusters. We will also study how these statistics can help account for a problem called intrinsic alignment, which can affect the accuracy of second- order lensing analyses. We will use observational data from previous surveys and data from the Euclid mission to test the new methods and develop a more accurate theoretical model. The expected improvements from applying third-order statistics to Euclid correspond to analyzing three additional Euclid-like surveys with second-order statistics alone. Consequently, the results of this study have the potential to significantly enhance our understanding of the Universe`s expansion history, its matter distribution and the behaviour of Dark Energy.