A Closer Look at Two $AdS_4$ Branes in an $AdS_5$ Bulk

TL;DR

This paper explores the dynamics of two $AdS_4$ branes within an $AdS_5$ bulk, analyzing how the position of the second brane affects graviton modes and the resulting gravitational physics.

Contribution

It reveals the importance of the warp factor's turn-around point in maintaining two graviton modes and describes how the graviton spectrum transitions as the second brane moves.

Findings

Both gravitons are significant when the second brane is near the warp factor's turn-around point.

The ultralight graviton mode becomes heavy as the second brane approaches this point.

The physics approaches the Randall-Sundrum model when the second brane is close to the turn-around.

Abstract

We investigate a scenario with two $AdS_4$ branes in an $AdS_5$ bulk. In this scenario there are two gravitons and we investigate the role played by each of them for different positions of the second brane. We show that both gravitons play a significant role only when the turn-around point in the warp factor is approximately equidistant from both branes. We find that the ultralight mode becomes heavy as the second brane approaches the turn-around point, and the physics begins to resemble that of the RS model. Thus we demonstrate the crucial role played by the turn-around in the warp factor in enabling the presence of both gravitons.