Extra dimensions seem to be an important ingredient for unification of gravity with quantum field theory. Our best candidate of quantum gravity, superstring theory, requires ten-dimensional space-time for mathematical consistency. However, since our world appears four-dimensional there must be a mechanism that "hides" extra dimensions so that we do not experience them at low energy scale. There are several methods in literature for concealing extra dimensions from our naked eye. In this thesis we only focus on two of them: braneworld scenario and flux compactification, both of which require the existence of the bulk fields.

This thesis investigates the role topological defects can play as bulk fields in higher-dimensional cosmology with different asymptotic topology. The first part deals with the non-singular braneworld: Skyrme branes and its higher dimensional generalizations. We show how these defects regularize the naked singularity around the core while at the same time approach the same flat-asymptotic behavior as the known thin-wall solutions. The second part is devoted to study an exotic transition, tunneling to (and from) nothing, in a landscape where the space-time vacua are direct products of X₄ × [special characters omitted], with X₄ can be: anti-de Sitter ( AdS₄), Minkowski (M₄), or de Sitter (dS₄). The tunneling is mediated by instanton solutions, via bubble nucleation. The bubble wall is smooth and magnetically-charged, and we show that this can be accomplished by having solitonic brane possessing magnetic charge, i.e., magnetic-monopole branes.