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

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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.