Quasiregular singularities taken seriously

I discuss a special class of singularities obtained as a natural 4-dimensional generalization of the conical singularity. Such singularities (called quasiregular) are ruinous for the predictive force of general relativity, so one often assumes (implicitly as a rule) that they can be somehow excluded from the theory. In fact, however, attempts to do so (without forbidding the singularities by fiat) have failed so far. It is advisable therefore to explore the possibility that their existence is not prohibited after all. I argue that quasiregular singularities, if allowed, may appear either in situations where causality is endangered or in the early Universe. In the latter case objects might appear strongly (though not quite) resembling cosmic strings. Those objects would be observable and, moreover, it is not impossible that we already do observe one.