  The usual account for the origin of cosmic structure during inflation is not
fully satisfactory, as it lacks a physical mechanism capable of generating the
inhomogeneity and anisotropy of our Universe, from an exactly homogeneous and
isotropic initial state associated with the early inflationary regime. The
proposal in [A. Perez, H. Sahlmann, and D. Sudarsky, Classical Quantum Gravity,
23, 2317, (2006)] considers the spontaneous dynamical collapse of the wave
function, as a possible answer to that problem. In this work, we review briefly
the difficulties facing the standard approach, as well as the answers provided
by the above proposal and explore their relevance to the investigations
concerning the characterization of the primordial spectrum and other
statistical aspects of the cosmic microwave background and large-scale matter
distribution. We will see that the new approach leads to novel ways of
considering some of the relevant questions, and, in particular, to distinct
characterizations of the non-Gaussianities that might have left imprints on the
available data.
