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.