Foreground Modeling in the Context of Cosmic Microwave Background

The ΛCDM model has been the standard model of cosmology for several decades. With the increasing precision of current and upcoming measurements, we now have a unique opportunity to test this model with greater significance. A central focus of modern cosmology is the search for evidence of cosmic inflation. Its most promising signature is the detection of a distinct pattern in the polarization of the CMB, known as primordial B-modes, which can only be generated by gravitational waves during the inflationary epoch. However, one of the critical challenges in detecting B-modes arises from foreground emissions within our Galaxy, which dominate the CMB signal. Current experiments lack the power to fully disentangle these foregrounds, making a definitive detection of inflation elusive. In this thesis, we aim at building upon current knowledge of foregrounds from observational data by developing a capability of simulating a diffuse foreground components that accurately captures their statistical properties. We focus specifically on thermal dust emission, which is one of the primary contaminants in polarized CMB signals. The first work consists in the development of the necessary estimators for measuring the level of non-Gaussianity using Minkowski functionals, in particular in the dust component which are currently in the PySM3 package, an algorithmic environment which gathers the efforts by the entire CMB community in order to understand, characterize, model and simulate foreground emissions. In the second work, we introduce ForSE+, a Python package based on Neural Networks, designed to generate non-Gaussian thermal dust emission maps at arcminute resolution and in polarization, using the available information from data, with the capability of producing random realizations of small-scale structures, a feature which is essential for implementing simulations in the ForSE+. We validate these maps to ensure that their statistical properties, including power spectra and non-Gaussianity, align with real observational data. These realistic simulations will be crucial for future studies of the impact of non-Gaussian foregrounds on CMB analysis, including lensing reconstruction, de-lensing, and the detection of cosmological gravitational waves in CMB polarization B-modes.They will significantly enhance the analysis of CMB data in upcoming experiments, such as those from the Simons Observatory and CMB-S4, ultimately pushing the boundaries of precision cosmology.