Inflation from field theory and string theory perspectives. Matter inflation and slow-walking inflation

This thesis is concerned with aspects of inflation both from a field theory and a string theory perspective. It aims at exploring new approaches to address the problem of moduli destabilization and the η-problem and to realize inflation in the matter sector. The first part is devoted to studying models of inflation in the framework of four-dimensional N=1 supergravity. We begin with investigating a new proposal to solve the problem of moduli destabilization, which seems to force us to choose between low-energy supersymmetry and high-scale inflation. This new approach is based on a particular way to couple the modulus to the F-term driving inflation. Using chaotic inflation with a shift symmetry as an example, we show that we can successfully combine low-energy supersymmetry and high-scale inflation. We construct a class of inflation models in N=1 supergravity where the inflaton resides in gauge non-singlet matter fields. These are extensions of a special class of hybrid inflation models, so-called tribrid inflation, where the η-problem can be solved by a Heisenberg symmetry. Compared to previously studied models, we have generalized our models with some inspiration from string theory. We investigate moduli stabilization during inflation and identify situations in which the inflaton slope is dominated by radiative corrections. We outline under which conditions this class of matter inflation models could be embedded into heterotic orbifold compactifications. In doing so, we suggest a new mechanism to stabilize some Kaehler moduli by F-terms for matter fields. In the second part, we consider models of warped D-brane inflation on a family of ten-dimensional supergravity backgrounds. We consider inflation along the radial direction near the tip of the warped throat and show that generically an inflection point arises for the inflaton potential, which is related to an inflection point of the dilaton profile. A universal scaling behaviour with the parameters of the model is exploited to extract the predictions for inflationary observables.