Quantum entanglement in de Sitter space with a wall and the decoherence of bubble universes

We study the effect of a bubble wall on the entanglement entropy of a free massive scalar field between two causally disconnected open charts in de Sitter space. We assume there is a delta-functional wall between the open charts. This can be thought of as a model of pair creation of bubble universes in dc Sitter space. We first derive the Euclidean vacuum mode functions of the scalar field in the presence of the wall in the coordinates that respect the open charts. We then derive the Bogoliubov transformation between the Euclidean vacuum and the open chart vacua that makes the reduced density matrix diagonal. We find that larger walls lead to less entanglement. Our result may be regarded as evidence of decoherence of bubble universes from each other. We also note an interesting relationship between our results and discussions of the black hole firewall problem.This work was supported in part by the MEXT KAKENHI Grants No. 15H05888 and No. 15K21733. S. K. was supported by IKERBASQUE, the Basque Foundation for Science and the Basque Government (Grant No. IT-979-16), and Spanish Ministry MINECO (Grant No. FPA2015-64041-C2-1P). A. A. was supported by a grant from University of California Davis and thanks A. Arrasmith for helpful conversations