Entanglement negativity in de Sitter biverse from Stringy Axionic Bell pair: An analysis using Bunch-Davies vacuum

Abstract

In this work, we study the signatures of quantum entanglement by computing entanglement negativity between two causally unrelated regions in $3+1$ dimensional global de Sitter space. We investigate a bipartite quantum field theoretic setup for this purpose, driven by an axionic Bell pair resulting from Type IIB string compactification on a Calabi-Yau three fold. We take into account a spherical surface that divides the spatial slice of the global de Sitter space into exterior and interior causally unrelated sub regions. For the computational purpose we use the simplest possible initial choice of quantum vacuum, which is Bunch-Davies state. The quantitative quantum information theoretic measure for entanglement negativity turns out be consistent with the results obtained for entanglement entropy, even we have to say it is better than that from quantum information theoretic point of view. We design the problem in a hyperbolic open chart where one of the causally unrelated observers remains constrained and the scale dependence enters to the corresponding quantum information theoretic entanglement measure for axionic Bell pair.We find from our analysis that in the large scales initially maximally entangled Bunch-Davies state turns out to be strongly entangled or weakly entangled depending on the axionic decay constant and the supersymmetry breaking scale. We also find that at the small scales the initial entanglement can be perfectly recovered.We also discuss the possibility of having a biverse picture, which is a mini version of the multiverse in the present theoretical set up. Last but not the least, we provide the necessary criteria for generating non vanishing quantum entanglement measures within the framework of quantum field theory of global de Sitter space as well as well as in primordial cosmology due to the axion derived from string theory.

96 pages, 17 figures, Updated version, Typos corrected, Accepted for publication in Fortschritte der Physik - Progress of Physics

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