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 analogue 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 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.

The Singularity Problem in Brane Cosmology

“…The asymptotic behaviour was found in Reference [6], Section 3.5. The envelope was derived in Reference [7], App.…”

“…All solutions of this system then become the integral curves of the three-dimensional, non-polynomial vector field [6],…”

“…However, to get this, one has to sacrifice an arbitrary constant, ending up with a family that does not correspond to a general solution of the field equations-at least for de Sitter branes, (for AdS branes there may be no such restriction) cf. [6], Section 2.2.…”

“…In this paper we provide a concise overview of the various ramifications and results that have been obtained in recent years about the singularity problem in such contexts, basically using the methods developed in References [6][7][8][9]. Previous work on this subject can be found in [10].…”

The large-scale structure of the ambient boundary

“…We know how to obtain a complete profile of all asymptotic situations that emerge when we have a bulk 5-geometry (V, g 5 ) containing an embedded 4-dimensional braneworld (M, g 4 ) that is either a 4-dimensional Minkowski, or de Sitter, or Anti-de Sitter spacetime, cf. [5]. In general, all asymptotic solutions have a form dictated by the method of asymptotic splittings [6].…”