Fermionic Bell violation in the presence of background electromagnetic fields in the cosmological de Sitter spacetime

TL;DR

This paper explores how background electromagnetic fields in de Sitter spacetime influence fermionic Bell inequality violations, revealing the impact of electric and magnetic fields on quantum entanglement and particle creation.

Contribution

It provides a detailed analysis of fermionic Bell violations in de Sitter space with electromagnetic backgrounds, highlighting the role of magnetic fields and extending to $ ext{alpha}$-vacua.

Findings

Bell violations occur for vacuum and entangled states.

Background electric fields influence particle creation and Bell violations.

Magnetic fields affect particle creation rates in curved spacetime.

Abstract

The violation of the Bell inequality for Dirac fermions is investigated in the cosmological de Sitter spacetime, in the presence of background electromagnetic fields of constant strengths. The orthonormal Dirac mode functions are obtained and the relevant in-out squeezed state expansion in terms of the Bogoliubov coefficients are found. We focus on two scenarios here : strong electric field and heavy mass limits (with respect to the Hubble constant). Using the squeezed state expansion, we then demonstrate the Bell violations for the vacuum and some maximally entangled initial states. Even though a background magnetic field alone cannot create particles, in the presence of background electric field and or spacetime curvature, it can affect the particle creation rate. Our chief aim thus here is to investigate the role of the background magnetic field strength in the Bell violation. Qualitative differences in this regard for different maximally entangled initial states are shown. Further extension of these results to the so called $\alpha$-vacua are also discussed.