Fresh inflation and decoherence of super Hubble fluctuations

I study a stochastic approach to the recently introduced fresh inflation model for super Hubble scales. I find that the state loses its coherence at the end of the fresh inflationary period as a consequence of the damping of the interference function in the reduced density matrix. This fact should be a consequence of a) the relative evolutions of both the scale factor and the horizon and b) the additional thermal and dissipative effects. This implies a relevant difference with respect to supercooled inflationary scenarios which require a very rapid expansion of the scale factor to give the decoherence of super Hubble fluctuations.