Scalar field localization on a brane with cosmological constant

TL;DR

This paper investigates how scalar fields can be localized on a brane with a cosmological constant in five-dimensional space, revealing bounds on the scalar mass that are relevant for brane stability and cosmology.

Contribution

It provides a new analysis of scalar field localization on a brane with a cosmological constant, deriving bounds on the scalar mass in terms of bulk mass and cosmological parameters.

Findings

Scalar fields can be localized with an upper mass bound.

The scalar mass bound depends on the bulk mass and cosmological constant.

Results have implications for brane stability and cosmological models.

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 $\lambda$ 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 $m^2=m_0^2+\alpha M^2\leq \beta |\lambda|$ with the calculable numbers $m_0^2, \alpha, \beta$. We point out that this result would be important to study the stability of the brane and cosmological problems based on the brane-world.