Characterizing Entanglement Entropy Produced by Non-Linear Scalar Interactions During Inflation

TL;DR

This paper explores how non-linear scalar interactions during inflation generate entanglement entropy between modes, affecting the quantum-to-classical transition of primordial fluctuations, with entropy scaling as a power law with coupling strength.

Contribution

It provides a detailed analysis of entanglement entropy production during inflation due to non-linear interactions, highlighting the scaling behavior and comparison of entanglement measures.

Findings

Entanglement entropy scales as S ∝ λ^{1.75} with coupling strength λ.

Non-linear effects produce entanglement between modes during inflation.

Mechanism is insufficient to fully explain classicality of fluctuations.

Abstract

The density fluctuations that we observe in the universe today are thought to originate from quantum fluctuations produced during a phase of the early universe called inflation. By evolving a wavefunction describing two coupled Fourier modes of a scalar field forward through an inflationary epoch, we demonstrate that non-linear effects can result in a generation of entanglement entropy between modes with different momenta in a scalar field during the inflationary period when just one of the modes is observed. Through this mechanism, the field would experience decoherence and appear more like a classical distribution today; however the mechanism is not sufficiently efficient to explain classicality. We find that the amount of entanglement entropy generated scales roughly as a power law S \propto \lambda^{1.75}, where \lambda is the coupling coefficient of the non-linear potential term. We also investigate how the entanglement entropy scales with the duration of inflation and compare various entanglement measures from the literature with the von Neumann entropy. This demonstration explicitly follows particle creation and interactions between modes; consequently, the mechanism contributing to the generation of the von Neumann entropy can be easily seen.