Cosmic strings and domain walls in models with Goldstone and pseudo Goldstone bosons

Topological vacuum structures are investigated in models with spontaneous breaking of exact and approximate global symmetries. The cosmological evolution of the structure is discussed. A spontaneous breaking of an exact global U(1) symmetry gives rise to vacuum strings which can produce cosmological density fluctuations leading to galaxy formation. In a simplified axion model, the vacuum structures are strings connected by domain walls. They decay before they can dominate the universe.