Conical singularities regularized in warped six-dimensional flux compactification and their induced brane cosmology

We discuss the regularization of codimension-2 singularities in warped six-dimensional Einstein-Maxwell axisymmetric models by replacing them by codimension-1 branes of a ring form, situated around the axis of symmetry. Further we consider the case of one capped regularized conical brane of codimension one and study the cosmological evolution which is induced on it as it moves in between the known {\it static} bulk and cap solutions. We present the resulting brane Friedmann equation which gives a dominant five-dimensional $\rho^2$ energy density term at high energies and a term linear to the energy density at low energies with, however, negative coefficient in the small four-brane radius limit (i.e. with negative effective Newton's constant)