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