Metric factorizability and equivalence of brane world models with Brans-Dicke theory

TL;DR

This paper demonstrates that in brane world models, the bulk metric can be factorized up to second order in a perturbative expansion, and shows the effective brane theory resembles Brans-Dicke gravity.

Contribution

It provides a perturbative proof of metric factorizability in brane models and links the effective brane dynamics to Brans-Dicke theory.

Findings

Metric factorizability holds up to second order in perturbation.

Nonlocal bulk terms can be replaced by a radion field.

Effective brane action resembles Brans-Dicke gravity.

Abstract

In the standard brane world models, the bulk metric ansatz is usually assumed to be factorizable in brane and bulk coordinates. However, it is not self-evident that it is always possible to factorize the bulk metric. Using the gradient expansion scheme, which involves the expansion of bulk quantities in terms of the brane-to-bulk curvature ratio, as a perturbative parameter, we explicitly show that metric factorizability is a valid assumption upto second order in the perturbative expansion. We also argue from our result that the same should be true for all orders in the perturbation scheme. We further establish that the nonlocal terms present in the bulk gravitational field equation can be replaced by the radion field; the effective action on the brane thereby obtained resembles the Brans-Dicke theory of gravity.