Entangled de Sitter from stringy axionic Bell pair I: an analysis using Bunch–Davies vacuum

In this work, we study the quantum entanglement and compute entanglement entropy in de Sitter space for a bipartite quantum field theory driven by an axion originating from Type IIB string compactification on a Calabi–Yau three fold ( CY³ ) and in the presence of an NS5 brane. For this computation, we consider a spherical surface S² , which divides the spatial slice of de Sitter ( dS₄ ) into exterior and interior sub-regions. We also consider the initial choice of vacuum to be Bunch–Davies state. First we derive the solution of the wave function of the 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 the entanglement entropy and Rényi entropy in $$3+1$$ dimension. Furthermore, we quantify the UV-finite contribution of the entanglement entropy which contain the physics of long range quantum correlations of our expanding universe. Finally, our analysis complements the necessary condition for generating non-vanishing entanglement entropy in primordial cosmology due to the axion.