Perturbative moduli stabilization and string inflation

This Master thesis is focused on the study of cosmological implications of type IIB string compactifications. In particular we will consider brane-antibrane inflation which is one of the first and most-studied realizations of inflation in string theory. The model however suffers from two main issues: ($i$) the lack of a fully supersymmetric formulation of the effective field theory in terms of a K\"ahler potential and a superpotential; ($ii$) the infamous $\eta$-problem due to the non-perturbative stabilization of the volume modulus. We will follow the idea of Burgess and Quevedo which proposed a supersymmetric formulation of the effective action of brane-antibrane inflation together with a mechanism to stabilize the volume mode at perturbative level based on RG-effects. In these perturbative corrections are however just field theory-inspired without a proper string theory motivation. In this Master thesis we will put these perturbative corrections on more solid grounds by exploiting all known results in $\alpha'$ and string loop corrections to the effective action of type IIB string compactifications. In this way we will improve the results of Burgess and Quevedo finding a way to stabilize the moduli in brane-antibrane inflation just using known perturbative corrections. Our results open up the possibility to implement a hybrid inflation scenario where the volume mode can act as a waterfall field to end inflation, leading to a post-inflation minimum where the supersymmetry breaking scale is much lower than the inflationary scale.