Entanglement entropy in a four-dimensional cosmological background

TL;DR

This paper calculates the holographic entanglement entropy for a thermalized conformal field theory in a four-dimensional, time-dependent cosmological background, revealing contributions related to thermal entropy and surface entanglement.

Contribution

It introduces a method to compute entanglement entropy in a dynamic, cosmological setting, extending previous static analyses to include expansion effects.

Findings

Identification of a volume term linked to thermal entropy

Discovery of area-proportional terms related to entanglement near the surface

Analysis of entanglement behavior across the cosmological horizon

Abstract

We compute the holographic entanglement entropy of a thermalized CFT on a time-dependent background in four dimensions. We consider a slab configuration extending beyond the cosmological horizon of a Friedmann-Lemaitre-Robertson-Walker metric. We identify a volume term that corresponds to the thermal entropy of the CFT, as well as terms proportional to the proper area of the entangling surface which are associated with strongly entangled degrees of freedom in the vicinity of this surface or with the expansion.