Entangled universes

TL;DR

This paper generalizes holographic entanglement entropy formulas to spacetimes with multiple asymptotic regions, including Minkowski, AdS, and de Sitter, proposing a new framework for understanding entanglement in complex universe models.

Contribution

It introduces a conjectured entanglement entropy formula applicable to spacetimes with multiple asymptotic regions, extending the HRT formula to new cosmological contexts.

Findings

The formula passes standard tests for holographic entanglement entropy.

Entanglement phase transitions are observed in Brill-Lindquist spacetimes.

Networks of universes are constructed using minimal surface gluing techniques.

Abstract

We propose a generalization of the RT and HRT holographic entanglement entropy formulas to spacetimes with asymptotically Minkowski as well as asymptotically AdS regions. We postulate that such spacetimes represent entangled states in a tensor product of Hilbert spaces, each corresponding to one asymptotic region. We show that our conjectured formula has the same general properties and passes the same general tests as the standard HRT formula. We provide further evidence for it by showing that in many cases the Minkowski asymptotic regions can be replaced by AdS ones using a domain wall. We illustrate the use of our formula by calculating entanglement entropies between asymptotic regions in Brill-Lindquist spacetimes, finding phase transitions similar to those known to occur in AdS. We construct networks of universes by gluing together Brill-Lindquist spaces along minimal surfaces. Finally, we discuss a variety of possible extensions and generalizations, including to universes with asymptotically de Sitter regions; in the latter case, we identify an ambiguity in the homology condition, leading to two different versions of the HRT formula which we call ``orthodox'' and ``heterodox'', with different physical interpretations.