  We investigate a new class of twisting type N vacuum solutions with nonzero
(positive) cosmological constant Lambda by studying the equations of geodesic
deviations along the privileged radial timelike geodesics, generalizing J.
Bicak and J. Podolsky's results on non-twisting type N solutions. It is shown
that these twisting radiative spacetimes can be interpreted as exact transverse
gravitational waves propagating in the de-Sitter universe, with a distinctive
feature that all the wave amplitudes are proportional to Lambda (dark
energy/matter source coupling). Moveover, we demonstrate the cosmic no-hair
conjecture in these spacetimes and discuss their Killing horizons.
