Brane-worlds in T-dual Bulks

TL;DR

This paper explores how T-duality transformations in a Schwarzschild-AdS black hole bulk affect brane-world cosmology, revealing invariances and dualities that connect bulk symmetries to brane scale factor behaviors.

Contribution

It demonstrates that T-duality in the bulk corresponds to scale factor duality on the brane when brane tension is included, unifying bulk and brane symmetries.

Findings

Scale factor is inverted under T-duality.

Either Friedmann or energy conservation equations remain unchanged.

Including brane tension makes T-duality equivalent to scale factor duality.

Abstract

We consider brane-world models with a Schwarzschild-AdS black hole bulk. In the particular case of a flat black hole horizon geometry, we study the behaviour of the brane cosmological equations when T-duality transformations act on the bulk. We find that the scale factor is inverted and that either the Friedmann equation or the energy conservation equation are unchanged. However, these become both invariant if we include a tension in the brane action. In this case, the T-duality in the bulk is completely equivalent to the scale factor duality on the brane.