Machine learning aided statistics of flux vacua and their cosmological applications

This thesis investigates targeted regions of the string landscape, focusing on Type IIB compactifications and their implications for moduli stabilization and cosmology. I develop a systematic algorithm for constructing flux vacua in finite regions of moduli space, demonstrating its effectiveness on a two-moduli Calabi-Yau threefold. This approach reveals local deviations from statistical expectations and intricate structures in vacuum distributions. Moreover, it enables the identification of phenomenologically promising solutions with small superpotential values at large complex structure and at tree-level, i.e. without non-perturbative effects. I also estimate the leading higher-derivative corrections to supergravity derived from Type IIB compactifications and assess their impact on LVS inflation models. Using the Kreuzer-Skarke database, I perform a classification for divisor topologies suitable to tame these higher-derivative corrections so that they do not ruin the flatness of the potential of existing string inflation models, focusing in particular on blow-up inflation, fibre inflation, and poly-instanton inflation. When these corrections are present, I show that they slightly modify the inflationary dynamics without however altering the predictions for the main cosmological observables.