Classification of inflationary models and constraints on fundamental
  physics
  This work is focused on the study of early time cosmology and in particular
on the study of inflation. After an introduction on the standard Big Bang
theory, we discuss the physics of CMB and we explain how its observations can
be used to set constraints on cosmological models. We introduce inflation and
we carry out its simplest realization by presenting the observables and the
experimental constraints that can be set on inflationary models. The
possibility of observing primordial gravitational waves (GWs) produced during
inflation is discussed. We present the reasons to define a classification of
inflationary models and introduce the \beta-function formalism for inflation by
explaining why in this framework we can naturally define a set of universality
classes for inflationary models. Theoretical motivations to support the
formulation of inflation in terms of this formalism are presented. Some
generalized models of inflation are introduced and the extension of the
\beta-function formalism for inflation to these models is discussed. Finally we
focus on the study of models where the (pseudo-scalar) inflaton is coupled to
some Abelian gauge fields that can be present during inflation. The analysis of
the problem is carried out by using a characterization of inflationary models
in terms of their asymptotic behavior. A wide set of theoretical aspects and of
observational consequences is discussed.
