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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:

?When the axion mass turns on, at time t1, each axion string becomes the edge of N domain walls

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?Since there are two or more exactly degenerate vacua and they have identical properties, the vacua

chosen at points outside each other’s causal horizon are independent of one another. Hence there is at least on the order of one domain wall per causal horizon at any given time.