Inflationary spectra and violation of Bell inequalities

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We point out that there exit operators, having a clear meaning in cosmology -- they select a given realization of the distribution of primordial density fluctuations --, which can violate Bell inequalities when evaluated in the ''standard'' inflationary quantum distribution. We then consider density matrices which describe partially decohered distributions and show how the importance of the violation decreases with the decoherence level. We determine the critical level beyond which no violation can be obtained. We argue that the corresponding density matrix is the quantum version of the stochastic ensemble used in numerical codes, and consisting of growing modes with random amplitudes.