  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.
