  In this thesis, we show how the structure of the landscape potential of the
primordial Universe may be probed through the primordial density perturbations
responsible for the origin of the cosmic microwave background anisotropies and
the large-scale structure of our Universe. Isocurvature fields may have
fluctuated across the barriers separating local minima of the landscape
potential during inflation. We analyze how this process could have impacted the
evolution of the primordial curvature perturbations. If the typical distance
separating consecutive minima of the landscape potential and the height of the
potential barriers are smaller than the Hubble expansion rate parametrizing
inflation, the probability distribution function of isocurvature fields becomes
non-Gaussian due to the appearance of bumps and dips associated with the
structure of the potential. We show that this non-Gaussianity can be
transferred to the statistics of primordial curvature perturbations. The type
of non-Gaussian structure that emerges in the distribution of curvature
perturbations cannot be fully probed with the standard methods of polyspectra;
instead, the probability distribution function is needed.
  To substantiate our claims, we offer a concrete model consisting of an
isocurvature perturbation with a sinusoidal potential and a linear derivative
coupling between the isocurvature and curvature field. This result is
generalized to arbitrary potentials and briefly studied beyond first-order
perturbation theory. Finally, we undertake a study of primordial
non-Gaussianity of the local type, where we use our results to reconstruct and
constrain the shape of the landscape potential with the help of Cosmic
Microwave Background observations by the Planck telescope and explore prospects
for observable quantities in the Large-Scale Structure of our universe towards
constraining its primordial statistics.
