Nonequilibrium quantum dynamics of phase transitions in an expanding universe

I summarize the derivation of a set of Feynman rules appropriate for the perturbative description of the nonequilibrium dynamics of the symmetry-breaking phase transition in $\lambda\phi^4$ theory in a Robertson-Walker universe. The approximation scheme I develop provides for a treatment of dissipative effects which are essential to an adequate description of the nonequilibrium state. It also provides for the emergence from an initially symmetric state of a final state exhibiting the properties of spontaneous symmetry breaking without the introduction by hand of any explicit symmetry breaking.