Entanglement between two disjoint universes

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.

Automated summary

The study utilizes the replica method to compute the entanglement entropy of a universe without gravity entangled with a disjoint gravitating universe in a quantum state. It reveals that at high entanglement temperatures, the island in the gravitating universe contributes to a bound on entanglement entropy in a manner akin to evaporating black holes. Additionally, it demonstrates that the entanglement wedge of the non-gravitating universe expands with increasing entanglement temperature, ultimately allowing for complete reconstruction of the gravitating universe.