Classification of inflationary models and constraints on fundamental physics.

In the first part of my seminar I propose a classification of inflationary models by using the most basic property of inflation: the approximate scaling invariance. This framework relies on the possibility of describing inflation in terms of a renormalization group equation. The slow rolling regime in this context is interpreted as the slow evolution close to a fixed point. In this framework we can thus explain in part the universality observed in the predictions of a certain number of inflationary models. In the second part of my seminar I consider the introduction of a generic coupling between the (pseudo-scalar) inflaton and some abelian gauge fields. In particular I discuss the possibility of generating an observable gravitational wave (GW) background and the possibility of generating a distribution of primordial black holes (PBH) which can account for part (or all) of Dark Matter (DM). The analysis is performed by dividing inflationary models into universality classes.