Vacuum state of the Dirac field in de Sitter space and entanglement entropy

We compute the entanglement entropy of a free massive Dirac field between two causally disconnected open charts in de Sitter space. We first derive the Bunch-Davies vacuum mode functions of the Dirac field. We find there exists no supercurvature mode for the Dirac field. We then give the Bogoliubov transformation between the Bunch-Davies vacuum and the open chart vacua that makes the reduced density matrix diagonal. We find that the Dirac field becomes more entangled than a scalar field as m(2)/H-2 becomes small, and the difference is maximal in the massless limit.We would like to thank Jiro Soda for valuable discussions, suggestions and comments. SK was supported by IKERBASQUE, the Basque Foundation for Science and the Basque Government (IT-979-16), and Spanish Ministry MINECO (FPA2015-64041-C2-1P). This work was supported in part by MEXT KAKENHI Nos. 15H05888, 15K21733, 24103001, 24103006, 15H02087 and 26287044