Four--dimensional Gravity from Singular Spaces

TL;DR

This paper explores how four-dimensional gravity is modified in brane-world models within supergravity, analyzing scalar-tensor theories, the attractor mechanism towards general relativity, and effects of matter on both branes.

Contribution

It provides a detailed derivation of the effective gravitational theory in singular space brane models, including the Brans-Dicke parameter and matter effects on the equivalence principle.

Findings

Existence of an attractor mechanism towards general relativity during matter domination.

Derivation of the Brans-Dicke parameter in brane-world scenarios.

Violation of the equivalence principle when matter is on both branes, influenced by extra-dimensional warping.

Abstract

The modification to four--dimensional Einstein gravity at low energy in two brane models is investigated within supergravity in singular spaces. Using perturbation theory around a static BPS background, we study the effective four--dimensional gravitational theory, a scalar--tensor theory, and derive the Brans--Dicke parameter when matter is present on the positive tension brane only. We show there is an attractor mechanism towards general relativity in the matter dominated era. The dynamics of the interbrane distance are discussed. Finally, when matter lives on both branes, we find that there is a violation of the equivalence principle whose magnitude is governed by the warping of the extra dimension.