  We apply the master equation with dynamical coarse graining approximation to
a pair of detectors interacting with a scalar field. By solving the master
equation numerically, we investigate evolution of negativity between comoving
detectors in de Sitter space. For the massless conformal scalar field, it is
found that a pair of detectors can perceive entanglement beyond the Hubble
horizon scale if the initial separation of detectors is sufficiently small. At
the same time, violation of the Bell-CHSH inequality on the super horizon scale
is also detected. For the massless minimal scalar field, on the other hand, the
entanglement decays within Hubble time scale owing to the quantum noise caused
by particle creations in de Sitter space and the entanglement on the super
horizon scale cannot be detected.
