Dynamical Localization of Gravity

TL;DR

This paper demonstrates how a 5D thick domain wall can produce a localized gravity brane similar to Randall-Sundrum models, with natural relations between cosmological constants and conditions for gravity localization.

Contribution

It explicitly derives the Randall-Sundrum brane as a thin wall limit of a thick domain wall and shows gravity localization conditions for both Minkowski and de Sitter branes.

Findings

Thin wall limit yields Randall-Sundrum brane with natural cosmological constant relation.

Gravity localization on de Sitter branes requires compactification of the extra dimension.

Net cosmological constant on the brane varies inversely with compactification radius.

Abstract

We show that the thin wall limit of the thick domain wall associated with a sine-Gordon soliton in a single non-compactified patch of 5-dimensional spacetime explicitly yields the Randall-Sundrum localized gravity two patch brane, with its discrete $Z_2$ symmetry arising from the discrete symmetry of the potential, and with the thin Minkowski brane $\Lambda_5+\kappa^2_5\Lambda^2_b/6=0$ relation between bulk and brane cosmological constants arising naturally without any need for fine tuning. Additionally we show that for an embedded thin de Sitter brane, localization of gravity is again possible provided the 5-space is compactified, with the now non-zero net cosmological constant $\Lambda_5+\kappa^2_5\Lambda^2_b/6$ on the brane being found to vary inversely with the compactification radius.