Telling tails in the presence of a cosmological constant

We study the evolution of massless scalar waves propagating on spherically symmetric spacetimes with a nonzero cosmological constant. Considering test fields on both Schwarzschild-de Sitter and Reissner-Nordstrom-de Sitter backgrounds, we demonstrate the existence of exponentially decaying tails at late times. Interestingly, the l = 0 mode asymptotes to a nonzero value, contrasting the asymptotically hat situation. We also compare these results, for l = 0, with a numerical integration of the Einstein-scalar field equations, finding good agreement between the two. Finally, the significance of these results to the study of the Cauchy horizon stability in black-hole-de Sitter spacetimes is discussed.