Abstract
Using the techniques of out-of-equilibrium field theory, westudy the influence on properties of cosmologicalperturbations generated during inflation on observable scalescoming from fluctuations corresponding today to scales muchbigger than the present Hubble radius. We write the effectiveaction for the coarse grained inflaton perturbations,integrating out the sub-horizon modes, which manifest themselves as a coloured noise and lead to memory effects. Usingthe 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. Ourbasic procedure shows that perturbations do preserve some memoryof the super-horizon scale dynamics, in the form ofscale dependent imprints in the statistical moments. Inparticular, we find a blue tilt of the power spectrum onlarge scales, in agreement with the recent results of theWMAP collaboration which show a suppression of the lowermultipoles in the cosmic microwave background anisotropies, anda substantial enhancement of the intrinsic non-Gaussianity on large scales.
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