Titolo della tesi: Stochastic Geometry Methods in Cosmology: Applications to Cosmic Microwave Background and Large Scale Structure data
The Cosmic Microwave Background (CMB) and the Large Scale Structure (LSS) of the Universe are two of the main cosmological observables that allow us to study the Early and Late Universe, respectively. With the growing amount of data expected to be observed from both probes in the coming years, a lot of attention has been directed towards developing new tools beyond isotropic correlation functions, both to extract cosmological information and check possible systematics in the data. In this work, we study and expand on some of these tools. First, we implement a method to detect the possible presence of residual contamination from extragalactic sources in the foreground–removed CMB maps; this algorithm uses needlet filtering and multiple testing statistics to achieve a nearly complete detection at ∼ 3.5σ, which we test with simulations and then apply to CMB data. Second, we adapt a ridge–finding algorithm to trace the Cosmic Filaments on LSS data; we boost the algorithm with a Machine Learning step and assess the characteristics of the produced catalogue, which is publicly available. Third, we propose a stacking procedure for Cosmic Filaments that preserves their anisotropic structure, and extensively test this procedure; we show that our Cosmic Filament catalogue presents high correlation with CMB gravitational lensing and other observables (up to SNR ≈ 9). Fourth, we describe the Minkowski Functionals for scalar maps and compute the theoretical expectation for isotropic Gaussian maps in T and P² CMB maps, as these tools can accurately measure deviations from these assumptions; we implement the software to compute these functionals and verify that simulations are in perfect agreement with the theoretical expectations. Fifth, we extend the Minkowski Functionals to spin 2 maps, such as the CMB polarisation, compute the theoretical expectations, implement the software to compute them and verify that simulations are in perfect agreement with the theoretical expectation. The tools and data produced in this work are (or will be soon) publicly available. This kind of tools can provide complementary information to the correlation functions (i.e., angular and matter power spectra), so in the future they can help in the study of cosmological problems, such as complex systematics in the data, non–linear evolution of structures, or primordial non–Gaussianities.