Manifestation of quantum entanglement between harmonic oscillators in a de Sitter background

Two harmonic oscillators interacting through the exchange of a quantum field leads to nonzero entanglement between the two, which is absent for classical interaction. In this work, we determine the entanglement between two such harmonic oscillators living in an expanding universe. It turns out that, if the oscillators are within the Hubble horizon, with their frequencies comparable to the rate of expansion of the Universe, the entanglement is nonzero and significant while, for oscillators outside the Hubble horizon, with oscillation frequencies much higher than the expansion rate, the entanglement is negligibly small.