Brane singularities and their avoidance

TL;DR

This paper investigates the conditions under which singularities in 3-brane models with scalar fields or perfect fluids can be avoided, revealing that brane curvature plays a crucial role in singularity behavior.

Contribution

It provides a comprehensive analysis of brane singularities using asymptotic splittings, highlighting how brane curvature and fluid parameters influence singularity avoidance.

Findings

Singularity avoidance in scalar field models requires curved branes.

For perfect fluids, singularities depend on the equation of state parameter b3.

Flat branes can be free of singularities for certain fluid parameters, supporting self-tuning.

Abstract

The singularity structure and the corresponding asymptotic behavior of a 3-brane coupled to a scalar field or to a perfect fluid in a five-dimensional bulk is analyzed in full generality using the method of asymptotic splittings. In the case of the scalar field, it is shown that the collapse singularity at a finite distance from the brane can be avoided only at the expense of making the brane world-volume positively or negatively curved. In the case where the bulk field content is parametrized by an analogue of perfect fluid with an arbitrary equation of state P=\gamma\rho between the `pressure' P and the `density' \rho, our results depend crucially on the constant fluid parameter \gamma: (i) For \gamma>-1/2, the flat brane solution suffers from a collapse singularity at finite distance, that disappears in the curved case. (ii) For \gamma<-1, the singularity cannot be avoided and it becomes of the big rip type for a flat brane. (iii) For -1<\gamma< or = -1/2, the surprising result is found that while the curved brane solution is singular, the flat brane is not, opening the possibility for a revival of the self-tuning proposal.