Decoherence during inflation: The generation of classical inhomogeneities

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.