Momentum-space Entanglement Entropy in De Sitter Spacetime

We study the momentum-space entanglement between the sub- and super-Hubble modes of a spectator scalar field, with a cubic $\ensuremath{\lambda}{\ensuremath{\phi}}^{3}$ 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 generalizing flat space results due to having a time-dependent interaction term and a nontrivial 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 [ , Entanglement entropy of cosmological perturbations, Phys. Rev. D 102, 043529 (2020)], which leads to interesting new questions.