Localization Issues for Robertson-Walker Branes

We discuss some of the localization issues associated with the embedding of Robertson-Walker type Randall-Sundrum branes in a bulk $AdS_5$. Specifically, we show that of the branes which are embeddable in $AdS_5$ the geometry associated with $M_4$ and $dS_4$ branes warps away from the brane while that associated with $AdS_4$ and $RW$ branes of any spatial 3-curvature antiwarps away from the brane. We discuss the gravitational fluctuations around an $M_4$ brane and analyze the specific role played by a delta function singularity at the brane. We show how a bulk sine-Gordon scalar field can without any fine-tuning naturally lead to localization of gravity around an $M_4$ brane.