Entanglement between two disjoint universes

TL;DR

This paper investigates the entanglement entropy between two disjoint universes, revealing how entanglement and wormholes influence the entropy and enable the reconstruction of the gravitating universe from the non-gravitating one.

Contribution

It introduces a novel calculation of entanglement entropy using the replica method with wormholes, showing the emergence of an island and a bound on entropy akin to Page curves.

Findings

The island coincides with a causal shadow region.

Entanglement entropy is bounded at high temperatures.

The non-gravitating universe's entanglement wedge can fully reconstruct the gravitating universe.

Abstract

We use the replica method to compute the entanglement entropy of a universe without gravity entangled in a thermofield-double-like state with a disjoint gravitating universe. Including wormholes between replicas of the latter gives an entropy functional which includes an "island" on the gravitating universe. We solve the back-reaction equations when the cosmological constant is negative to show that this island coincides with a causal shadow region that is created by the entanglement in the gravitating geometry. At high entanglement temperatures, the island contribution to the entropy functional leads to a bound on entanglement entropy, analogous to the Page behavior of evaporating black holes. We demonstrate that the entanglement wedge of the non-gravitating universe grows with the entanglement temperature until, eventually, the gravitating universe can be entirely reconstructed from the non-gravitating one.