  The understanding of the primordial mechanism that seeded the cosmic
structures we observe today in the sky is one of the major goals in cosmology.
The leading paradigm for such a mechanism is provided by the inflationary
scenario, a period of violent accelerated expansion in the very early stages of
evolution of the Universe. While our current knowledge of the physics of
inflation is limited to phenomenological models which fit observations, an
exquisite understanding of the particle content and interactions taking place
during inflation would provide breakthroughs in our understanding of
fundamental physics at high energies. In this review, we summarize recent
theoretical progress in the modelling of the imprint of primordial interactions
in the large scale structures of the Universe. We focus specifically on the
effects of such interactions on the statistical distribution of dark matter
halos, providing a consistent treatment of the steps required to connect the
correlations generated among fields during inflation all the way to the
late-time correlations of halos.
