Quantum entanglement in de Sitter space from Stringy Axion: An analysis using $\alpha$ vacua

Abstract

In this work, we study the phenomena of quantum entanglement by computing de Sitter entanglement entropy from von Neumann measure. For this purpose we consider a bipartite quantum field theoretic setup in presence of axion originating from $\mathbf{Type}\mathbf{II}\mathbf{B}$ string theory. We consider the initial vacuum to be CPT invariant non-adiabatic $\alpha$ vacua state under $\mathbf{SO}(1,4)$ ismometry, which is characterized by a real one-parameter family. To implement this technique we use a ${\mathbf{S}}^2$ which divide the de Sitter into two exterior and interior sub-regions. First, we derive the wave function of axion in an open chart for $\alpha$ vacua by applying Bogoliubov transformation on the solution for Bunch-Davies vacuum state. Further, we quantify the density matrix by tracing over the contribution from the exterior region. Using this result we derive entanglement entropy, R$\acute{e}$nyi entropy and explain the long-range quantum effects in primordial cosmological correlations. We also provide a comparison between the results obtained from Bunch-Davies vacuum and the generalized $\alpha$ vacua, which implies that the amount of quantum entanglement and the long-range effects are larger for non zero value of the parameter $\alpha$. Most significantly, our derived results for $\alpha$ vacua provides the necessary condition for generating non zero entanglement entropy in primordial cosmology.

31 pages, 13 figures, Revised version, Accepted for publication in Nuclear Physics B

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