D-brane inflation with perturbative moduli stabilisation

Cosmological inflation is a period of accelerated expansion of the early universe. Nowadays there are plenty of inflationary models which agree with experimental constraints but a complete microscopic understanding of this quasi de Sitter phase is still missing. In this thesis, after reviewing the present situation in Cosmology and Supersymmetry, we present the main possibilities to embed inflation in a UV complete framework coming from String Theory. In particular, we present the main virtues and limitations of RG-induced modulus stabilisation, focusing on D3-antiD3 inflation and discussing whether slow-roll can be obtained in the regime of validity of the effective field theory.