Entanglement and correlations between local observables in de Sitter spacetime

TL;DR

This paper investigates how curvature in de Sitter spacetime affects local quantum field entanglement, revealing that increased curvature enhances correlations but reduces entanglement between local modes, with implications for cosmic inflation.

Contribution

It introduces a fully local approach to analyze entanglement in de Sitter space, challenging previous entropy-based interpretations and clarifying the spatial distribution of entanglement.

Findings

Increased curvature boosts correlations between local modes.

Counterintuitively, increased curvature decreases entanglement.

A tiny cosmological constant qualitatively changes the vacuum's entanglement structure.

Abstract

Studies of quantum field entanglement in de Sitter space based on the von Neumann entropy of local patches have concluded that curvature enhances entanglement between regions and their complements. Similar conclusions about entanglement enhancement have been reached in analyses of Fourier modes in the cosmological patch of de Sitter space. We challenge this interpretation by adopting a fully local approach: examining entanglement between pairs of field modes compactly supported within de Sitter's cosmological patch. Our approach is formulated in terms of the properties of a metric tensor and an associated complex structure induced by the Bunch-Davies vacuum on the classical phase space. We find that increasing curvature increases correlations between local modes but, somewhat counterintuitively, decreases their entanglement. Our methods allow us to characterize how entanglement is spatially distributed, revealing that a cosmological constant, even if tiny, qualitatively alters the vacuum's entanglement structure. We show that our results are compatible with previous entropy-based studies when properly interpreted. Our findings have implications for entanglement between observables generated during cosmic inflation.