  We show how the quantum to classical transition of the cosmological
fluctuations produced during inflation can be described by means of the
influence functional and the master equation. We split the inflaton field into
the system-field (long-wavelength modes), and the environment, represented by
its own short-wavelength modes. We compute the decoherence times for the
system-field modes and compare them with the other time scales of the model. We
present the renormalized stochastic Langevin equation for an homogeneous
system-field and then we analyze the influence of the environment on the power
spectrum for some modes in the system.

General Relativity and Quantum Cosmology;Astrophysics;High Energy Physics - Phenomenology;High Energy Physics - Theory