Naked Singularity and Gauss-Bonnet Term in Brane World Scenarios

TL;DR

This paper explores how adding a Gauss-Bonnet term and a dilaton potential to the Einstein-Hilbert action impacts brane world models, aiming to address the cosmological constant problem and analyze scalar field configurations.

Contribution

It introduces a novel approach combining Gauss-Bonnet corrections and dilaton potentials in brane world scenarios, deriving first order equations without supersymmetry.

Findings

Dilaton potential is bounded below for positive Gauss-Bonnet coefficient.

The dilaton field forms a kink solution in the extra dimension.

The approach provides new solutions relevant to the cosmological constant problem.

Abstract

We add a Gauss-Bonnet term to the Einstein-Hilbert action and study the recent proposal to solve the cosmological constant problem. We also consider the possibility of adding a dilaton potential to the action. In the absence of supersymmetry, we obtain first order Bogomol'nyi equation as a solution-generating method in our scenario. When the coefficient of the Gauss-Bonnet term is positive, the dilaton potential is bounded below. Assuming a simple double-well potential, the dilaton field is found to be a kink in the fifth dimension.