Entanglement entropy in de Sitter space

TL;DR

This paper calculates the entanglement entropy for quantum fields in de Sitter space, revealing how it encodes long-range correlations due to cosmic expansion, using both free and strongly coupled theories.

Contribution

It provides the first detailed analysis of entanglement entropy in de Sitter space for both free and holographic strongly coupled fields, highlighting dimension-dependent features.

Findings

In even dimensions, entanglement entropy scales with the number of e-foldings.

In odd dimensions, the entropy is contained in a finite part.

Entanglement captures long-range correlations from cosmic expansion.

Abstract

We compute the entanglement entropy for some quantum field theories on de Sitter space. We consider a superhorizon size spherical surface that divides the spatial slice into two regions, with the field theory in the standard vacuum state. First, we study a free massive scalar field. Then, we consider a strongly coupled field theory with a gravity dual, computing the entanglement using the gravity solution. In even dimensions, the interesting piece of the entanglement entropy is proportional to the number of e-foldings that elapsed since the spherical region was inside the horizon. In odd dimensions it is contained in a certain finite piece. In both cases the entanglement captures the long range correlations produced by the expansion.