  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.
