Quantum correlations in inflationary spectra and violation of Bell inequalities

In spite of the macroscopic character of the fluctuation amplitudes, we show that the standard inflationary distribution of primordial density fluctuations still exhibits inherently quantum mechanical correlations (which cannot be mimicked by any classical stochastic ensemble). To this end, we propose a Gedanken experiment for which certain Bell inequalities are violated. We also compute the effect of decoherence and show that the violation persists provided that the decoherence lies below a certain non-vanishing threshold. Moreover, there exists a higher threshold above which no violation of any Bell inequalities can occur, so that the corresponding distributions can be interpreted as stochastic ensembles of classical fluctuations.