Based on the formalism of spontaneous symmetry breaking, Tom Kibble developed the idea for the primordial fluctuations of a two-component scalar field like the Higgs field. If a two-component scalar field switches from the isotropic and homogeneous high-temperature phase to the symmetry-broken stage during cooling and expansion of the very early universe (shortly after Big Bang), the order parameter necessarily cannot be the same in regions which are not connected by causality. Regions are not connected by causality if they are separated far enough (at the given age of the universe) that they cannot "communicate" even with the speed of light. This implies that the symmetry cannot be broken globally. The order parameter will take different values in causally disconnected regions, and the domains will be separated by domain walls after further evolution of the universe. Depending on the symmetry of the system and the symmetry of the order parameter, different types of topological defects like monopoles, vortices or textures can arise. It was debated for quite a while if magnetic monopoles might be residuals of defects in the symmetry-broken Higgs field. Up to now, defects like this have not been observed within the event horizon of the visible universe. This is one of the main reasons (beside the isotropy of the cosmic background radiation and the flatness of spacetime) why nowadays an inflationary expansion of the universe is postulated. During the exponentially fast expansion within the first 10 second after Big-Bang, all possible defects were diluted so strongly that they lie beyond the event horizon. Today, the two-component primordial scalar field is usually named inflaton.