Primordial black holes in string inflation

In this thesis we consider the production of primordial black holes (PBH) in the context of single field inflation with the aim of describing a significant fraction of dark matter. In the models we consider, the inflaton is a string modulus and its potential is typical of type IIB fibre inflation. The potential presents a plateau at CMB scales and an extremely flat region on smaller scales. The background is analysed by solving the Friedmann's and the Klein-Gordon equations for the system. Perturbations are introduced through the usual Mukhanov-Sasaki equation for the gauge invariant curvature perturbations, whose solution allows us to find the primordial power spectrum which is then compared to observations. In the class of models considered there is an often occurring tension between the tilt of the scalar power spectrum and observations. We study this tension and propose mechanisms to minimise it. We modify the form of the fibre inflationary potential, modifying therefore the slope of the ultra slow-roll plateau. We find that a better agreement with the experimentally measured value of the spectral index can be reached. Therefore that tension between the value of the spectral index on CMB scale and the power spectrum enhancement on PBH scales can be explained as a consequence of the class of potential taken into account. This tension can be avoided in models that provide a different plateau form.