I am having some problems with understanding what it means to be in the horizon of something else. In particular I'm looking into axion cosmology model. In this paper, and in particular in the strings and wall decay sections: http://arxiv.org/abs/astro-ph/0610440 Let me try to elaborate some of the ideas. When PQ symmetry is broken and after QCD phase transition it gets broken: [itex]U(1) \rightarrow Z(N)[/itex], I think that this means that in the mexican hat potential, the flat direction becomes like this: /\/\/\/\/\/\/\/\ with N sharp points. Between these points there are created the strings, correct? If not, what does he mean by: ? Also in the same paragraph he takes [itex]N \ge 2[/itex] so at least the flat direction gets at least two spikes along its way (/\/\): So I am wondering, why is that "hence" true? the domain wall appears in the field's configuration space, and not in the general spacetime...any help?