Entangled de Sitter from Stringy Axionic Bell pair I: An analysis using Bunch Davies vacuum

TL;DR

This paper investigates quantum entanglement in de Sitter space within string theory, focusing on axion fields from Type IIB compactification, and explores implications for Bell inequality violations in cosmology.

Contribution

It provides a detailed analysis of entanglement entropy for axionic fields in de Sitter space using Bunch Davies vacuum, including derivations of wave functions and density matrices.

Findings

Computed entanglement and Rényi entropy in 3+1 dimensions.

Quantified UV finite contributions related to long-range quantum correlations.

Linked entanglement entropy to conditions for Bell inequality violation in early universe.

Abstract

In this work, we study the quantum entanglement and compute entanglement entropy in de Sitter space for a bipartite quantum field theory driven by axion originating from ${\bf Type~ IIB}$ string compactification on a Calabi Yau three fold (${\bf CY^3}$) and in presence of ${\bf NS5}$ brane. For this compuation, we consider a spherical surface ${\bf S}^2$, which divide the spatial slice of de Sitter (${\bf dS_4}$) into exterior and interior sub regions. We also consider the initial choice of vaccum to be Bunch Davies state. First we derive the solution of the wave function of axion in a hyperbolic open chart by constructing a suitable basis for Bunch Davies vacuum state using Bogoliubov transformation. We then, derive the expression for density matrix by tracing over the exterior region. This allows us to compute entanglement entropy and R$\acute{e}$nyi entropy in $3+1$ dimension. Further we quantify the UV finite contribution of entanglement entropy which contain the physics of long range quantum correlations of our expanding universe. Finally, our analysis compliments the necessary condition for the violation of Bell's inequality in primordial cosmology due to the non vanishing entanglement entropy for axionic Bell pair.