  In this paper, we show how the structure of the landscape potential of the
primordial Universe may be probed through the properties of the primordial
density perturbations responsible for the origin of the cosmic microwave
background anisotropies and the large-scale structure of our Universe.
Isocurvature fields -fields orthogonal to the inflationary trajectory- 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 to the
structure of the potential. We show that this non-Gaussianity can be
transferred to the statistics of primordial curvature perturbations if the
isocurvature fields are coupled to the 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. The latter is
obtained by summing all the $n$-point correlation functions. To substantiate
our claims, we offer a concrete model consisting of an axionlike isocurvature
perturbation with a sinusoidal potential and a linear derivative coupling
between the isocurvature and curvature fields. In this model, the probability
distribution function of the curvature perturbations consists of a Gaussian
function with small superimposed oscillations reflecting the isocurvature axion
potential.
