Interpretation of twisting type N vacuum solutions with cosmological constant

We investigate a new class of twisting type N vacuum solutions with nonzero (positive) cosmological constant Λ by studying the equations of geodesic deviations along the privileged radial timelike geodesics, generalizing J Bičák and J Podolský'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 Λ. Moreover, we demonstrate the cosmic no-hair conjecture in these spacetimes and discuss their Killing horizons.