Entanglement of Quantum Fluctuations in the Inflationary Universe

TL;DR

This paper studies how quantum entanglement of scalar fields during inflation diminishes over large distances, leading to classical behavior, by analyzing bipartite entanglement and covariance matrices.

Contribution

It introduces a lattice model and applies separability criteria to quantify entanglement decay across the Hubble horizon during inflation.

Findings

Entanglement disappears when regions exceed the Hubble horizon.

Classicality emerges as a consequence of entanglement loss.

Condition for classical distribution is linked to symplectic eigenvalues.

Abstract

We investigate quantum entanglement of a scalar field in the inflationary universe. By introducing a bipartite system using a lattice model of scalar field, we apply the separability criterion based on the partial transpose operation and numerically calculate the bipartite entanglement between separate spatial regions. We find that the initial entangled state becomes separable or dis-entangled when the size of the spatial regions exceed the Hubble horizon. This is necessary condition for the appearance of classicality of the quantum fluctuation. We further investigate the condition for the appearance of the classical distribution function and find that the condition is given by the inequality for the symplectic eigenvalue of the covariance matrix of the scalar field.