Axions, Domain Walls, and the Early Universe

Axion models have a spontaneously broken $Z\left(N\right)\mathrm{}$ symmetry. The resulting discretely degenerate vacua and domain-wall solitons are incompatible with the standard cosmology. It is possible, however, to introduce a small $Z\left(N\right)\mathrm{}$ 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.