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 purpose of this brief report is to present some results of our on-going project on the asymptotic behaviour of braneworld-type solutions on approach to their possible finite 'time' singularities. Cosmological singularities in such frameworks have served as means to attack the cosmological constant problem (see 1 and references therein). The main mathematical tool of our analysis is the method of asymptotic splittings introduced in Ref. 2Below we study a model consisting of a 3−brane configuration embedded in a five dimensional bulk space with a scalar field being minimally coupled to the bulk and conformally coupled to the fields restricted on the brane. The total action is taken to be S total = S bulk + S brane , where

The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows one to determine the singularity structure of the solutions. The result is applied to brane-worlds consisting of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid parameterizing a generic class of bulk matter. We find that all flat brane solutions suffer from a finite-distance singularity contrary to previous claims. We then study the possibility of avoiding finite-distance singularities by cutting the bulk and gluing regular solutions at the position of the brane. Further imposing physical conditions such as finite Planck mass on the brane and positive energy conditions on the bulk fluid, excludes, however, this possibility as well.

By extending previous analysis of the authors, a systematic study of the singularity structure and possible asymptotic behaviors of five-dimensional braneworld solutions is performed in the case where the bulk is a mixture of an analog of perfect fluid (with a density and pressure depending on the extra coordinate) and a massless scalar field. The two bulk components interact by exchanging energy so that the total energy is conserved. In a particular range of the interaction parameters, we find flat brane general solutions avoiding the singularity at finite distance from the brane, in the same region of the equation of state constant parameter $\gamma=P/\rho$ that we found previously in the absence of the bulk scalar field $(-1<\gamma<-1/2)$.Comment: 48 page

We show that globally and regularly hyperbolic future geodesically incomplete isotropic universes, except for the standard all-encompassing 'big crunch', can accommodate singularities of only one kind, namely, those having a non-integrable Hubble parameter, H. We analyze several examples from recent literature which illustrate this result and show that such behaviour may arise in a number of different ways. We also discuss the existence of new types of lapse singularities in inhomogeneous models, impossible to meet in the isotropic ones.