Abstract
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.
Highlights
We study spacetime singularities in a general five-dimensional braneworld with curved branes satisfying four-dimensional maximal symmetry
In previous work we studied the singularity structure of a braneworld model consisting of a flat 3-brane embedded in a five-dimensional bulk space filled with an analogue of a perfect fluid
The last possible case is that of an open universe with positive density support on the bulk, which translates to considering C > 0 and k < 0 (AdS braneworld)
Summary
In previous work we studied the singularity structure of a braneworld model consisting of a flat 3-brane embedded in a five-dimensional bulk space filled with an analogue of a perfect fluid (the fifth coordinate Y playing the role of time). A way to avoid such singularities is to exploit the natural Z2 symmetry introduced by the existence of the brane by cutting the bulk space and considering a slice of it which is free from finite-distance singularities This matching mechanism is possible for all values of γ , the requirement for localised gravity on the brane restricts γ in the interval (−2, −1). A question that naturally arises is whether any of the above conclusions about the existence of singularities are sensitive to the geometry of the brane so that singularities are absent when we consider a curved brane (regular solutions with curved branes with a cosmological constant or a scalar field, with a particular emphasis to inflation, were previously considered in [2,3]) It was proposed in [4,5] that the singularity present in the flat brane model moves to infinite distance when the brane becomes curved, such as de Sitter (dS) or anti-de Sitter (AdS) in the maximally symmetric case, which was in accordance with previous claims made in [6].
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