  Massive perturbations in asymptotic flat black holes leave a distinct
signature in their late-time evolution `tail': an oscillatory behavior
modulated by the Compton wavelength of the field, which can be associated with
the so-called quasibound state spectrum. In asymptotically de-Sitter
spacetimes, however, the massive perturbations always leak to the cosmological
horizon, which indicates the absence of a quasibound part of the spectrum. In
this work, we show that an additional mode exists in asymptotically de-Sitter
black holes that produces an imprint similar to that of the quasibound states
in the late-time behavior of massive scalar perturbations. If the Compton
wavelength is larger than a certain critical value (which depends on the
cosmological constant), the oscillatory behavior of the tail turns into an
exponential decay due to the fact that the de-Sitter mode is purely imaginary.
Even for black holes with typical length scales small in comparison to the size
of the cosmological horizon, the late-time tail behavior of the massive
perturbations is modified as compared to the usual $t^{-5/6}$ for Schwarzschild
black holes, thus being a distinctive feature induced by the presence of a
cosmological constant.
