De Sitter candidates from flux compactifications

In this talk I will explain recent and ongoing progress in the construction of de Sitter cosmologies using Calabi-Yau flux compactifications of type IIB string theory. In particular, I will present fully explicit solutions, at leading order in the $\alpha’$ and $g_s$ expansions, that realize de Sitter vacua along the lines envisioned by Kachru, Kallosh, Linde and Trivedi. I will furthermore argue that the (quasi-)limit of vanishing flux superpotential in this class of flux compactifications is equivalent to the large volume limit of M-theory compactified on suitable 7-manifolds with $G_2$ holonomy.