Critical dynamics of symmetry breaking: Quenches, dissipation, and cosmology

Symmetry-breaking phase transitions may leave behind topological defects with a density dependence on the quench rate. We investigate the dynamics of such quenches for the one-dimensional, Landau-Ginzburg case and show that the density of kinks, $n,$ scales differently with the quench time scale, ${\tau }_Q,$ depending on whether the dynamics in the vicinity of the critical point is overdamped $\left(n\propto {\tau }_Q^{-1/4}\right)$ or underdamped $\left(n\propto {\tau }_Q^{-1/3}\right).\mathrm{}$ Either of these cases may be relevant to the early Universe, and we derive bounds on the initial density of topological defects in cosmological phase transitions.