Localizing modes of massive fermions and a U(1) gauge field in the inflating baby-Skyrmion branes

We consider the six-dimensional brane world model, where the brane is described by a localized solution to the baby-Skyrme model extending in the extra dimensions. The branes have a cosmological constant modeled by inflating four-dimensional slices and we further consider a bulk cosmological constant. We focus on the topological number three solutions and discuss the localization mechanism of the fermions on the above 3-branes. We discuss interpretation of the model in term of quark third-generation mass and in terms of the inflation history. We argue that the model can describe various epochs of the early Universe by suitably choosing the parameters. We further discuss the localization properties of gauge fields on the brane and argue that this is achieved only for specific values of the electromagnetic coupling, providing a quantization to the electric charge.