Vacuum State of the Dirac Field in de Sitter Space and Entanglement Entropy

TL;DR

This paper calculates the entanglement entropy of a Dirac field in de Sitter space, revealing that fermionic fields exhibit greater entanglement than scalar fields, especially in the massless limit.

Contribution

It derives the Dirac field's vacuum mode functions in de Sitter space and analyzes its entanglement properties, highlighting differences from scalar fields and the absence of supercurvature modes.

Findings

Dirac field has no supercurvature modes in de Sitter space.

Entanglement entropy increases as the mass-to-Hubble ratio decreases.

Fermionic fields are more entangled than scalar fields in the massless limit.

Abstract

We compute the entanglement entropy of a free massive Dirac field between two causally disconnected open charts in de Sitter space. We first derive the Bunch-Davies vacuum mode functions of the Dirac field. We find there exists no supercurvature mode for the Dirac field. We then give the Bogoliubov transformation between the Bunch-Davies vacuum and the open chart vacua that makes the reduced density matrix diagonal. We find that the Dirac field becomes more entangled than a scalar field as $m^2/H^2$ becomes small, and the difference is maximal in the massless limit.