Spontaneously broken symmetries play a key role in elementary particle physics. All the known fundamental forces of nature (except for gravity) can be described by renormalizable gauge theories, and the only viable mechanism for giving matter masses in these theories is spontaneous symmetry breaking. In almost all theories with spontaneous symmetry breaking the symmetry is restored at the high temperatures of the early Universe. This results in a cosmological phase transition as the Universe cools through the critical temperature at which the symmetry becomes broken [Linde(1979), Vilenkin and Shellard(1994), Kibble(1980)].
Over much of its history, the evolution of the Universe appears to have been "adiabatic", with matter in local thermal equilibrium. However, phase transitions often involve very long timescale processes that can drop out of local equilibrium and lead to interesting effects. For example one can have domain formation, as local regions make different choices of symmetry breaking direction. Topological defects such as domain walls, magnetic monopoles, or cosmic strings form where domains meet. Complete equilibrium is only achieved when the domains grow (or "coarsen") until the Universe is covered by a single domain, but the coarsening process can take longer than the present age of the Universe to complete. Thus there can be out-of-equilibrium processes that continue right through to the present day. Topological defects typically have interior energy densities similar to the ambient energy density when they were first formed, even after the surrounding matter density has dropped by many orders of magnitude due to cosmic expansion. Thus defects can preserve a region with the high densities of the very early Universe to the present day, offering a unique window on ultra-high energy physics.
With or without the formation of long-lived defects, the out-of-equilibrium processes in cosmic phase transitions can lead to a wide variety of interesting effects. In some cases these effects introduce exciting new possibilities into the field of cosmology. In other cases the results of phase transitions are in clear conflict with observations, firmly ruling out any model that has that type of transition. The notorious "monopole problem" [Preskill(1979)] ruled out almost all models of Grand Unification that were popular at that time. Guth's studies of the very same phase transitions led to his seminal paper on cosmic inflation [Guth(1981)].
Cosmic phase transitions could have had a variety of important roles, from creating baryon number, to producing high energy cosmic rays, "wimp-zillas", and a potentially observable background of gravitational radiation. For a time, they provided a viable competing picture for the origin of cosmic structure. In this section we review the current status and future opportunities.