Ifigeneia Klaoudatou

We review studies on the singularity structure and asymptotic analysis of a 3-brane (flat or curved) embedded in a five-dimensional bulk filled with a ‘perfect fluid’ with an equation of state p = γ ρ , where p is the ‘pressure’ and ρ is the ‘density’ of the fluid, depending on the fifth space coordinate. Regular solutions satisfying positive energy conditions in the bulk exist only in the cases of a flat brane for γ = − 1 or of AdS branes for γ ∈ [ − 1 , − 1 / 2 ) . More cases can be found by gluing two regular brunches of solutions at the position of the brane. However, only a flat brane for γ = − 1 leads to finite Planck mass on the brane and thus localizes gravity. In a more recent work, we showed that a way to rectify the previous findings and obtain a solution for a flat brane and a range of γ , which is both free from finite-distance singularities and compatible with the physical conditions of energy and finiteness of four-dimensional Planck mass, is by introducing a bulk fluid component that satisfies a nonlinear equation of state of the form p = γ ρ λ with γ < 0 and λ > 1 . This article is part of the theme issue ‘The future of mathematical cosmology, Volume 2’.

We study spacetime singularities in a general five-dimensional braneworld with curved branes satisfying four-dimensional maximal symmetry. The bulk is supported by an analog of perfect fluid with the time replaced by the extra coordinate. We show that contrary to the existence of finite distance singularities from the brane location in any solution with flat (Minkowski) branes, in the case of curved branes there are singularity-free solutions for a range of equations of state compatible with the null energy condition.

The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows one to dete

The existence of envelopes is studied for systems of differential equations in connection with the method of asymptotic splittings which allows to determine the singularity structure of the solutions. The result is applied to braneworlds consisting of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid parametrizing 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.