Characterizing entanglement entropy produced by nonlinear scalar interactions during inflation

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 wave function describing two coupled Fourier modes of a scalar field forward through an inflationary epoch, we demonstrate that nonlinear 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 $S\ensuremath{\propto}{\ensuremath{\lambda}}^{1.75}$, where $\ensuremath{\lambda}$ is the coupling coefficient of the nonlinear 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.