Axions, Domain Walls, and the Early Universe

Axion models have a spontaneously broken $Z(N)$ symmetry. The resulting discretely degenerate vacua and domain-wall solitons are incompatible with the standard cosmology. It is possible, however, to introduce a small $Z(N)$ breaking interaction into axion models without upsetting the Peccei-Quinn mechanism. In that case the domain walls disappear a certain time after their formation in the early universe. Their presence for a limited time period might lead to galaxy formation.