Quasibound state reminiscent in de-Sitter black holes: Quasinormal modes and the decay of massive fields

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.