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=c1M^2 + c2 with positive constants c1 and c2 for the AdS brane. We discuss the relation of these results to the stability of the brane and also some cosmological problems.