We have studied the existence and stability properties of defects (domain walls and vortices) with non-symmetric core and non-trivial winding at infinity. These defects arise in scalar field theories that exhibit an explicit breaking of a global symmetry, for domain wall and for vortices. In their spectrum and for a particular range of parameters topologically stable and unstable defects appear with either symmetric or non-symmetric cores. Possible implications for the cosmology of the early universe are the following: With regard to the case of domain walls with a symmetric core (saddle and high Napoleon hat potentials) a possible embedding of such configurations in a realistic Higgs electroweak model may realize a new mechanism for baryogenesis at the electroweak phase transition. Defect mediated baryogenesis has been so far only successfully implemented at scales introduced near or above the electroweak one (Brandenberger et al. (1996)). These mechanisms are based on unsuppressed B+L violating sphaleron transitions taking place in the symmetric core of the defects during scattering processes (Cohen et al. (1993)). As a result of our work the question of existence of electroweak domain walls with a symmetric core now translates to whether in the most general electroweak Lagrangian with two Higgs doublets potential energies of the ``saddle hat'' or ``high Napoleon hat'' type exist for an appropriate range of parameters. As the parity symmetry in these models is broken both spontaneously an explicitly the expected domain walls in their spectrum are certainly of the non-topological type. Moreover it would be of interest to see if such defects arise at a second order electroweak phase transition. Our observation of non-spherical collapse of wall bubbles with non-symmetric core may imply that the domain wall network simulations need to be re-examined for parameter ranges where a non-symmetric core in energetically favoured.
With regard to our demonstration of existence of vortices with non-symmetric core it becomes immediately suggestive the existence of a new kind of a bosonic superconducting string, possessing massive charge carriers (Witten (1985)). This would be the case if our model is properly coupled to a gauge field.The physics of fermions introduced to such a system is also open for investigation. The astrophysical and cosmological role of superconducting strings has been extensively investigated in the literature (Ostriker et al. (1986), Davis & Shellard (1988), Davis & Shellard (1988)).