Abstract
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.
Highlights
In a previous work [1], we studied and classified the singularity structure and the corresponding asymptotic behavior of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid, using the so-called method of asymptotic splittings [2,3]
We found a surprising result that the flat brane solution does not suffer from a finite-distance singularity in the region −1 < γ ≤ −1/2, opening the possibility of the self-tuning mechanism for the physical cosmological constant
In the first part of this paper, we studied the effect that the existence of envelopes brings into the dynamics of the cosmological model of [1], consisting of a 3-brane embedded in a five-dimensional fluid bulk satisfying an analog of an
Summary
In a previous work [1], we studied and classified the singularity structure and the corresponding asymptotic behavior of a 3-brane in a five-dimensional bulk, in the presence of an analog of a bulk perfect fluid, using the so-called method of asymptotic splittings [2,3]. We assumed that the bulk fluid satisfies an equation of state p = γρ, with a constant parameter γ , while the ‘pressure’ p and the ‘density’ ρ are functions of the fifth coordinate Y. We found a surprising result that the flat brane solution does not suffer from a finite-distance singularity in the region −1 < γ ≤ −1/2, opening the possibility of the self-tuning mechanism for the physical cosmological constant
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