Coarse-grained field wave function in stochastic inflation

TL;DR

This paper investigates the quantum-to-classical transition of matter field fluctuations during inflation by analyzing the coherence of a coarse-grained wave function in a power-law universe, identifying conditions for classical stochastic behavior.

Contribution

It provides a detailed analysis of the phase-space coherence of matter fluctuations in stochastic inflation, highlighting the conditions under which classical stochastic descriptions become valid.

Findings

Coherence persists for certain parameters in power-law inflation.

Classical stochastic treatment is invalid when the system remains coherent.

For p > 4.6, the system loses coherence and classical approximation applies.

Abstract

The wave function for the matter field fluctuations in the infrared sector is studied within the framework of inflationary cosmology. These fluctuations are described by a coarse-grained field which takes into account only the modes with wavelength much bigger than the size of the Hubble horizon. The case of a power-law expanding universe is considered and it is found that the relevant phase-space remains coherent under certain circumstances. In this case the classical stochastic treatment for matter field fluctuations is not valid, however, for $p > 4.6$, the system loses its coherence and a classical stochastic approximation is allowed.