During inflation, quantum vacuum fluctuations are amplified and stretched to large distances, giving rise to cosmological perturbations that seed the large scale structure of our Universe. However, astronomers usually analyse the data with purely classical techniques and apparently never need to rely on the quantum formalism to understand them. So is there observational signatures of the quantum nature of inflationary perturbations?
I will first show that the quantum discord of cosmological perturbations produced during an era of inflation is large, denoting large quantum correlations. I will then discuss the possibility to carry out Bell-type experiments on cosmological perturbations. Finally, I will show that if one wants to describe primordial perturbations with a state that contains no quantum correlations, one necessarily introduces specific non-Gaussianities, the non-detection of which would provide the ultimate test.