Scalar field localization on a brane with cosmological constant

We investigate the localization of a massive scalar for both dS and AdS branes, where the scalar mass is varied from the massive-particle region to the tachyon region. We find that the eigenmass m of the localized mode satisfies a simple relation m(2) = cM(2) with a positive constant c for the dS brane, and m(2) = c(1)M(2) + c(2) with positive constants c(1) and c(2) for the AdS brane. We discuss the relation of these results to the stability of the brane and also some cosmological problems.