Vacua in String Theory : de Sitter Space and Stability in Flux Compactifications

Our understanding of cosmology has evolved radically in the last decades. Current models demand the presence of dark energy in our universe and the most favored candidate behind this component is a small positive cosmological constant that characterizes a de Sitter (dS) spacetime. Simultaneously, theoretical physicists have stood up to the challenge of building a consistent theory of quantum gravity and string theory has raised as a strong contender. In this thesis we present some explorations within supergravity, a low energy limit of string theory, studying non-supersymmetric vacua, its stability, and the possibility of finding dS. We study the landscape of flux compactifications to produce dS with non-geometric fluxes. We find precise analytic procedures to find perturbatively stable dS near supersymmetric and no-scale Minkowski in a potential derived from type IIB compactifications. We also provide analytical evidence of naked singularities being produced in supergravity backgrounds after the introduction of anti-Dp-branes, at both vanishing and finite temperature. In order to study the problem of semi-classical stability, we explore compactifications with anti-de Sitter as external space. We argue that truncations to closed-string-sector excitations of non-supersymmetric theories may be non-perturbatively protected by the existence of globally defined fake-superpotentials if they are perturbatively stable, a reasoning that goes in line with the standard positive energy theorems. We find that non-supersymmetric solutions tend to manifest modes with masses under the Breitenlohner-Freedman bound once the open-string-sector is explored while supersymmetric solutions remain stable. We see this as a hint in the nature of the instabilities predicted by the weak gravity conjecture