The ordering of scalar fields after a phase transition in which a group $G$ of global symmetries is spontaneously broken to a subgroup $H$ provides a possible explanation for the origin of structure in the Universe, as well as leading to observable effects in condensed-matter systems. The field dynamics can depend, in principle, on the geometry and topology of the vacuum manifold $G/H;$ for example, texture configurations which collapse and unwind will exist if the third homotopy group ${\pi }_3\mathrm{}(G/H)\mathrm{}$ is nontrivial. We numerically simulate the evolution of texturelike configurations in a number of different models, in order to determine the extent to which the geometry and topology of the vacuum manifold influence the field evolution. We find that the dynamics is affected by whether or not the theory supports strings or monopoles [characterized by ${\pi }_1\mathrm{}(G/H)\mathrm{}$ and ${\pi }_2\mathrm{}(G/H),$ respectively]. In some of the theories studied, configurations with initially spherically symmetric energy densities are unstable to nonspherical collapse; these theories are also found to nucleate defects during the collapse. Models that do not support monopoles or strings behave similarly to each other, regardless of the specific vacuum manifold.

• Received 30 January 1997

DOI:https://doi.org/10.1103/PhysRevD.55.6454