  In spite of the macroscopic character of the primordial fluctuations, the
standard inflationary distribution (that obtained using linear mode equations)
exhibits inherently quantum properties, that is, properties which cannot be
mimicked by any stochastic distribution. This is demonstrated by a Gedanken
experiment for which certain Bell inequalities are violated. These violations
are {\it in principle} measurable because, unlike for Hawking radiation from
black holes, in inflationary cosmology we can have access to both members of
correlated pairs of modes delivered in the same state. We then compute the
effect of decoherence and show that the violations persist provided the
decoherence level (and thus the entropy) lies below a certain non-vanishing
threshold. Moreover, there exists a higher threshold above which no violation
of any Bell inequality can occur. In this regime, the distributions are
``separable'' and can be interpreted as stochastic ensembles of fluctuations.
Unfortunately, the precision which is required to have access to the quantum
properties is so high that, {\it in practice}, an observational verification
seems excluded.
