Entanglement in De Sitter Space

TL;DR

This paper explores generalized holographic entanglement entropy formulas in de Sitter space, applying two proposals and analyzing their consistency with expected results, highlighting the need for further understanding of holographic thermodynamics.

Contribution

It introduces and compares the monolayer and bilayer proposals for holographic entanglement entropy in de Sitter space, extending previous AdS-based formulas.

Findings

Both proposals often agree on results.

They sometimes disagree, indicating unresolved issues.

Further research needed on holographic thermodynamics.

Abstract

This paper expands on two recent proposals, \cite{Susskind:2021dfc}\cite{Susskind:2021esx} and \cite{Shaghoulian:2021cef}, for generalizing the Ryu-Takayanagi and Hubeny-Rangamani-Takayanagi formulas to de Sitter space. The proposals (called the monolayer and bilayer proposals) are similar; both replace the boundary of AdS by the boundaries of static-patches--in other words event horizons. After stating the rules for each, we apply them to a number of cases and show that they yield results expected on other grounds. The monolayer and bilayer proposals often give the same results, but in one particular situation they disagree. To definitively decide between them we need to understand more about the nature of the thermodynamic limit of holographic systems.