Quantum entanglement in de Sitter space from stringy axion: An analysis using α 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 set up for axion field, previously derived from Type II B string theory compactified to four dimensions. We consider the initial vacuum to be CPT invariant non-adiabatic α vacua state under SO(1,4) isometry, which is characterised by a real one-parameter family. To implement this technique we use a S2 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 α 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, Rényi entropy and explain the long-range quantum effects in primordial cosmological correlations. Our results for α vacua provides the necessary condition for generating non zero entanglement entropy in primordial cosmology.