Early and late time cosmology of type IIB flux compactifications

We explore various aspects of type IIB flux compactifications, focusing on the stabilisation of moduli and the implications for cosmology. We present a novel method to obtain type IIB flux vacua with flat directions at tree level, implemented in both toroidal and Calabi-Yau compactifications. We also estimate the leading higher derivative corrections to $\N=1$ supergravity and their impact on moduli stabilisation and inflation models. Additionally, we develop realizations of Early Dark Energy (EDE) within type IIB string theory, identifying promising candidates for resolving the Hubble Tension. Finally, we analyse the joint distribution of the gravitino mass and the cosmological constant in KKLT and LVS models, highlighting the favourable conditions for lower scales of supersymmetry breaking.