Bounds on curved domain walls in 5d gravity

TL;DR

This paper investigates the possibility of curved domain wall solutions in five-dimensional dilaton gravity, establishing constraints and bounds on curvature based on dilaton coupling and boundary conditions, with implications for the cosmological constant problem.

Contribution

It provides new bounds on curved domain walls in 5d gravity, extending previous results by analyzing general dilaton-dependent brane tensions and their curvature limits.

Findings

No curved deformations for special dilaton coupling.

Curvature bounded by the Kaluza-Klein scale for general dilaton-dependent tension.

Confirmed previous results using symmetry arguments.

Abstract

We discuss maximally symmetric curved deformations of the flat domain wall solutions of five-dimensional dilaton gravity that appeared in a recent approach to the cosmological constant problem. By analyzing the bulk field configurations and the boundary conditions at a four-dimensional maximally symmetric curved domain wall, we obtain constraints on such solutions. For a special dilaton coupling to the brane tension that appeared in recent works, we find no curved deformations, confirming and extending slightly a result of Arkani-Hamed et al which was argued using a $Z_2$-symmetry of the solution. For more general dilaton-dependent brane tension, we find that the curvature is bounded by the Kaluza-Klein scale in the fifth dimension.