Decoherence of gauge-invariant metric fluctuations during inflation

TL;DR

This paper investigates how gauge-invariant metric fluctuations during inflation decohere over time, showing that super Hubble perturbations lose quantum coherence due to environmental interactions, affecting early universe quantum states.

Contribution

It models the decoherence process of metric fluctuations during inflation using a stochastic harmonic oscillator framework, highlighting the loss of quantum coherence in super Hubble modes.

Findings

Super Hubble metric perturbations lose coherence by the end of inflation.

Decoherence arises from interference with the conjugate variable due to environmental interaction.

The wave function evolution is described by a Schrödinger equation with a time-dependent effective Hamiltonian.

Abstract

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.