Scalar field localization on a brane with cosmological constant

Abstract

We address the localization of a scalar field, whose bulk-mass M is considered in a wide range including the tachyonic region,on a three-brane. The brane with non-zero cosmological constant $λ$ is embedded in five dimensional bulk space. We find in this case that the trapped scalar could have mass $m$ which has an upper bound and expressed as $m^2=m_0^2+αM^2\leq β|λ|$ with the calculable numbers $m_0^2, α, β$. We point out that this result would be important to study the stability of the brane and cosmological problems based on the brane-world.