Momentum-space entanglement entropy in de Sitter

TL;DR

This paper investigates how momentum-space entanglement entropy behaves for a scalar field in de Sitter space, revealing rapid growth and new subtleties due to curved spacetime effects and time-dependent interactions.

Contribution

It extends the understanding of momentum-space entanglement to curved spacetime, specifically de Sitter, highlighting new features and growth behavior not seen in flat space.

Findings

Momentum-space entanglement entropy grows rapidly in de Sitter.

New subtleties arise from time-dependent interactions and vacuum states.

Results support previous findings on cosmological perturbations.

Abstract

We study the momentum-space entanglement between the sub- and super-Hubble modes of a spectator scalar field, with a cubic $\lambda \phi^3$ interaction, in de Sitter space. Momentum-space entanglement has some universal properties for any interacting quantum field theory, and we examine them for this specific curved background using the Hubble scale as a natural delimiter to define UV/IR separation. We show that there are several new subtleties when generalising flat space results due to having a time-dependent interaction term and a non-trivial vacuum state. Our main finding is that the momentum-space entanglement entropy in de Sitter space grows very rapidly, supporting previous similar results for cosmological perturbations [1], which leads to interesting new questions.