  Using the techniques of out-of-equilibrium field theory, we study the
influence on the properties of cosmological perturbations generated during
inflation on observable scales coming from fluctuations corresponding today to
scales much bigger than the present Hubble radius. We write the effective
action for the coarse-grained inflaton perturbations integrating out the
sub-horizon modes, which manifest themselves as a colored noise and lead to
memory effects. Using the simple model of a scalar field with cubic
self-interactions evolving in a fixed de Sitter background, we evaluate the
two- and three-point correlation function on observable scales. Our basic
procedure shows that perturbations do preserve some memory of the
super-horizon-scale dynamics, in the form of scale-dependent imprints in the
statistical moments. In particular, we find a blue tilt of the power-spectrum
on large scales, in agreement with the recent results of the WMAP collaboration
which show a suppression of the lower multipoles in the Cosmic Microwave
Background anisotropies, and a substantial enhancement of the intrinsic
non-Gaussianity on large scales
