  Inflationary cosmological perturbations of quantum-mechanical origin
generically interact with all degrees of freedom present in the early Universe.
Therefore, they must be viewed as an open quantum system in interaction with an
environment. This implies that, under some conditions, decoherence can take
place. The presence of the environment can also induce modifications in the
power spectrum, thus offering an observational probe of cosmic decoherence.
Here, we demonstrate that this also leads to non Gaussianities that we
calculate using the Lindblad equation formalism. We show that, while the
bispectrum remains zero, the four-point correlation functions become
non-vanishing. Using the Cosmic Microwave Background measurements of the
trispectrum by the Planck satellite, we derive constraints on the strength of
the interaction between the perturbations and the environment and show that, in
some regimes, they are more stringent than those arising from the power
spectrum.
