  We investigate classical and quantum correlations of a quantum field in the
inflationary universe using a particle detector model. By considering the
entanglement and correlations between two comoving detectors interacting with a
scalar field, we find that the entanglement between the detectors becomes zero
after their physical separation exceeds the Hubble horizon. Furthermore, the
quantum discord, which is defined as the quantum part of total correlation,
approaches zero on super horizon scale. These behaviors support appearance of
classical nature of the quantum fluctuation generated during the inflationary
era.
