Comments on conformal stability of brane-world models

TL;DR

This paper examines the stability of 5-D brane-world models under conformal perturbations, revealing that Poincare and de Sitter branes are unstable while Anti de Sitter branes are stable, with implications for effective constants and hierarchies.

Contribution

It provides a comprehensive analysis of conformal stability in brane-world models, identifying stability conditions and hierarchy effects on physical constants.

Findings

Poincare and de Sitter branes are unstable due to negative gravexciton mass squared.

Anti de Sitter branes are stable with positive gravexciton mass squared.

Effective cosmological and gravitational constants vary across different branes.

Abstract

The stability of 5-D brane-world models under conformal perturbations is investigated. The analysis is carried out in the general case and then it is applied to particular solutions. It is shown that models with the Poincare and the de Sitter branes are unstable because they have negative mass squared of gravexcitons whereas models with the Anti de Sitter branes have positive gravexciton mass squared and are stable. It is also shown that 4-D effective cosmological and gravitational constants on branes as well as gravexciton masses undergo hierarchy: they have different values on different branes.