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

TL;DR

This paper investigates quantum entanglement in de Sitter space using string-inspired axion fields and generalized $oldsymbol{ extalpha}$ vacua, revealing how entanglement varies with vacuum parameters and impacts primordial cosmological correlations.

Contribution

It introduces a novel analysis of de Sitter entanglement entropy considering stringy axions and non-adiabatic $oldsymbol{ extalpha}$ vacua, highlighting the role of vacuum choice in quantum correlations.

Findings

Entanglement entropy is larger for non-zero $oldsymbol{ extalpha}$ vacua.

Long-range quantum effects are enhanced in $oldsymbol{ extalpha}$ vacua.

Non-zero entanglement entropy is possible in primordial cosmology with $oldsymbol{ extalpha}$ 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 ${\bf Type~ II~B}$ string theory. We consider the initial vacuum to be CPT invariant non-adiabatic $\alpha$ vacua state under ${\bf SO(1,4)}$ ismometry, which is characterized by a real one-parameter family. To implement this technique we use a ${\bf S^2}$ 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.