Brane World Models And Darboux Transformations

TL;DR

This paper applies Darboux transformations to 5-D brane world models with a scalar field, deriving new exact solutions that generalize the Randall-Sundrum model, especially in static cases.

Contribution

It introduces a novel method using Darboux transformations to find exact solutions in brane world models with scalar fields, extending previous solutions.

Findings

Derived new exact solutions via Darboux transformations.

Generalized the Randall-Sundrum solution.

Applicable to models with cosmological expansion.

Abstract

We consider a 5-D gravity plus a bulk scalar field, and with a 3-brane. The Darboux transformation is used to construct some exact solutions. To do this we reduce the system of equations, which describes the 5-D gravity and bulk scalar field to the Schr\"odinger equation. The jump conditions at the branes lead to the jump potential in the Schr\"odinger equation. Using the Darboux transformation with these jump conditions, we offer a new exact solution of the brane equations, which represents a generalization of the Rundall-Sundrum solution. For simplicity, the main attention is focused on the case when Hubble root on the visible brane is zero. However, the argument is given that our method is valid in more realistic models with cosmological expansion.