Uniqueness of RS2 type thick branes supported by a scalar field

TL;DR

This paper investigates the properties and uniqueness of thick RS2-type branes supported by scalar fields in 5D, revealing their AdS asymptotics, specific potential constraints, and issues with matter confinement.

Contribution

It demonstrates the universal AdS asymptotics of thick branes, establishes conditions on the scalar potential for regularity, and analyzes the matter confinement problem.

Findings

Thick branes always have AdS asymptotics far from the brane.

Scalar potential V(φ) must have an alternating sign and satisfy a fine-tuning condition.

Stress-energy tensor of test scalar field diverges at the AdS horizon, posing confinement issues.

Abstract

We study thick brane world models as Z_2-symmetric domain walls supported by a scalar field with an arbitrary potential V(\phi) in 5D general relativity. Under the global regularity requirement, such configurations (i) have always an AdS asymptotic far from the brane, (ii) are only possible if V(\phi) has an alternating sign and (iii) V(\phi) should satisfy a certain fine-tuning type equality. Thus a thick brane with any admissible V(\phi) is a regularized version of the RS2 brane immersed in the AdS_5 bulk. The thin brane limit is realized in a universal manner by including an arbitrary thick brane model in a one-parameter family, where the parameter "a" is associated with brane thickness; the asymptotic value of V(\phi) (related to \Lambda_5, the effective cosmological constant) remains a-independent. The problem of ordinary matter confinement on the brane is discussed for a test scalar field. Its stress-energy tensor is found to diverge at the AdS horizon for both thin and thick branes, making a serious problem for this class of brane world models.