De Sitter Holography and Entanglement Entropy

TL;DR

This paper explores a holographic duality for de Sitter space involving two coupled CFTs, demonstrating that their entanglement entropy aligns with the Gibbons-Hawking de Sitter entropy and analyzing its time evolution.

Contribution

It introduces a new de Sitter holography model with coupled CFTs, showing the entanglement entropy reproduces de Sitter horizon entropy and analyzing the entanglement structure.

Findings

Entanglement entropy matches Gibbons-Hawking formula.

Identifies a relevant finite CFT Hilbert space with Cardy behavior.

Derives maximally mixed state from CFT interactions.

Abstract

We propose a new example of entanglement knitting spacetime together, satisfying a series of checks of the corresponding von Neumann and Renyi entropies. The conjectured dual of de Sitter in d+1 dimensions involves two coupled CFT sectors constrained by residual d-dimensional gravity. In the d=2 case, the gravitational constraints and the CFT spectrum are relatively tractable. We identify a finite portion of each CFT Hilbert space relevant for de Sitter. Its maximum energy level coincides with the transition to the universal Cardy behavior for theories with a large central charge and a sparse light spectrum, derived by Hartman, Keller, and Stoica. Significant interactions between the two CFTs, derived previously for other reasons, suggest a maximally mixed state upon tracing out one of the two sectors; we derive this by determining the holographic Renyi entropies. The resulting entanglement entropy matches the Gibbons-Hawking formula for de Sitter entropy, including the numerical coefficient. Finally, we interpret the Gibbons-Hawking horizon entropy in terms of the Ryu-Takayanagi entropy, and explore the time evolution of the entanglement entropy.