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

Understand

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.