Statistical mechanics of soft-boson phase transitions

The existence of structures on large (say, 100 Mpc) scales and limits to anisotropies in the cosmic microwave background radiation (CMBR) have imperiled models of structure formation based solely upon the standard cold-dark-matter scenario. Novel scenarios, which may be compatible with large-scale structure and small CMBR anisotropies, invoke nonlinear fluctuations in the density appearing after recombination, accomplished via the use of late-time phase transitions involving ultralow-mass scalar bosons. Here, we study the statistical mechanics of such phase transitions in several models involving naturally ultralow-mass pseudo Nambu-Goldstone bosons (PNGB's). These models can exhibit several interesting effects at high temperature, which we argue are the most general possibilities for PNGB's.