  Since it was confirmed two decades ago that the expansion of the Universe is
accelerating, it would be of theoretical interests to figure out what is the
influence from cosmological constant on detection of stochastic gravitational
wave background. This paper studies the overlap reduction functions in
de-Sitter space-time for a pair of one-way tracking gravitational wave
detectors. It is shown to be non-trivial in an expanding Universe, because the
propagation of light along line of sight also has effect on the response of GW
detectors. It is found that the expansion of the Universe can enhance the value
of magnitude of the overlap reduction functions, when the detector pairs are
close to each other. For nanohertz gravitational waves, this effect can
dominate the values of overlap reduction functions when the galactic pulsar
pairs are separated by milliarcsecond.
