Dark radiation and observable gravity waves from string inflation

In this thesis we work on a model of string inflation called fibre inflation. We investigate whether this inflationary model can predict a tensor-to-scalar-ratio of order 0.01 which might be detectable in the near future. The main constraint comes from the amount of axionic dark radiation produced from the inflaton decay at reheating. Very light axions are a generic feature of 4D string models and behave as extra neutrino species. We first analyze the inflationary dynamics and derive the predictions for the spectral index and the tensor-to-scalar ratio r as a function of the number of e-foldings under the requirement of generating the correct measured amplitude of the density perturbations. We then focus on reheating. We start by computing the inflaton couplings to all particles in our model: MSSM fields in the visible sector and light axions belonging to the hidden sector. This computation allows us to derive the dominant inflaton decay channels which are into Higgses, gauge bosons and light axions. In turn, these decay rates lead to a clear prediction for the amount of dark radiation in terms of extra neutrino species of about 0.5-0.6. These values require approximately 57 e-foldings which can allow for a spectral index almost 1.000 and a tensor-to-scalar-ratio around 0.01 in agreement with Planck observations in the presence of extra dark radiation. We finally point out that, due to the high inflationary scale , the supersymmetry breaking scale turns out to be too high to yield a correct Higgs mass around 125 GeV. This tension can be easily overcome if the visible sector is a simple extension of the MSSM like the NMSSM.