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

TL;DR

This paper investigates how a bubble wall in de Sitter space affects quantum entanglement and decoherence between bubble universes, revealing that larger walls reduce entanglement and may cause decoherence.

Contribution

It models the impact of a delta-functional wall on entanglement entropy in de Sitter space, deriving vacuum modes and Bogoliubov transformations in this context.

Findings

Larger walls decrease entanglement entropy.

The wall induces decoherence between bubble universes.

Results relate to black hole firewall discussions.

Abstract

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 de 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.