Abstract

I studied the gauge-invariant fluctuations of the metric during inflation. In the infrared sector the metric fluctuations can be represented by a coarse-grained field. I can write a Schr\"odinger 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 also studied 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.

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