Dynamical Instability of Brane Solutions with a Self-Tuning Cosmological Constant

TL;DR

This paper investigates the stability of a five-dimensional brane-world model with a scalar field aimed at addressing the cosmological constant problem, revealing instabilities and the challenges of energy conservation in dynamic solutions.

Contribution

It demonstrates the instability of the original self-tuning brane solution and explores time-dependent generalizations, highlighting issues with energy conservation and boundary conditions.

Findings

Original solution is a saddle point and unstable.

Constructed exact time-dependent solutions show non-conservation of energy.

Adding a bulk scalar potential complicates boundary conditions, affecting the self-tuning mechanism.

Abstract

A five-dimensional solution to Einstein's equations coupled to a scalar field has been proposed as a partial solution to the cosmological constant problem: the effect of arbitrary vacuum energy (tension) of a 3-brane is cancelled; however, the scalar field becomes singular at some finite proper distance in the extra dimension. We show that in the original model with a vanishing bulk potential for the scalar, the solution is a saddle point which is unstable to expansion or contraction of the brane world. We construct exact time-dependent solutions which generalize the static solution, and demonstrate that they do not conserve energy on the brane; thus they do not have an effective 4-D field theoretic description. When a bulk scalar field potential is added, the boundary conditions on the brane cannot be trivially satisfied, raising hope that the self-tuning mechanism may still give some insight into the cosmological constant problem in this case.