  I study the gauge-invariant fluctuations of the metric during inflation. In
the infrared sector the metric fluctuations can be represented by a
coarse-grained field. We can write a Schroedinger equation for the
coarse-grained metric fluctuations which is related to an effective Hamiltonian
for a time dependent parameter of mass harmonic oscillator with a stochastic
external force. I study the wave function for a power-law expanding universe. I
find that the phase space of the quantum state for super Hubble scalar metric
perturbations loses its coherence at the end of inflation. This effect is a
consequence of interference between the super Hubble metric perturbations and
its canonical conjugate variable, which is produced by the interaction of the
coarse-grained scalar metric fluctuation with the environment.
