Brane singularities and their avoidance

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 analog of perfect fluid with an arbitrary equation of state P = γρ between the ‘pressure’ P and the ‘density’ ρ, our results depend crucially on the constant fluid parameter γ. (i) For γ > −1/2, the flat brane solution suffers from a collapse singularity at a finite distance that disappears in the curved case. (ii) For γ < −1, the singularity cannot be avoided and it becomes of the big rip type for a flat brane. (iii) For −1 < γ ⩽ −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.