Cosmological correlation functions in scalar and vector inflationary
  models
  This thesis is centered on three main subjects within the theory of inflation
and cosmological perturbations: loop corrections to the power spectrum of
curvature fluctuations generated during inflation; evolution of cosmological
fluctuations in anisotropic pre-inflationary cosmologies; statistical
anisotropy and non-Gaussianity predictions of models of inflation populated
with vector fields. Currently, what makes even more interesting the study of
2-nd and higher order corrections to cosmological correlation functions as well
as the computation of higher-than-two order correlators, is the almost
unprecedented chance to confront theories with new and increasingly accurate
experimental data that will shed more light in the physics of the early
Universe. In the context of loop calculations, we have computed the corrections
arising from scalar-tensor interactions in models of single-field inflation
(both for the standard slow-roll model and for models described by Lagrangians
with non-canonical kinetic terms). In the context of anisotropic cosmologies,
also motivated by the observation of "anomalies" in the Cosmic Microwave
Background (CMB) fluctuations, we have computed the bispectrum and the
trispectrum of the curvature fluctuations in inflationary models with SU(2)
vector fields, analyzing the statistical anisotropy features of the correlators
in these models; finally, we have studied cosmological perturbations for a
Universe with a Bianchi type-I background metric, with an energy density
dominated by a pressureless fluid and in the presence of a cosmological
constant.
