  A complete set of Feynman rules is derived, which permits a perturbative
description of the nonequilibrium dynamics of a symmetry-breaking phase
transition in $\lambda\phi^4$ theory in an expanding universe. In contrast to a
naive expansion in powers of the coupling constant, this approximation scheme
provides for (a) a description of the nonequilibrium state in terms of its own
finite-width quasiparticle excitations, thus correctly incorporating
dissipative effects in low-order calculations, and (b) the emergence from a
symmetric initial state of a final state exhibiting the properties of
spontaneous symmetry breaking, while maintaining the constraint $<\phi>\equiv
0$. Earlier work on dissipative perturbation theory and spontaneous symmetry
breaking in Minkowski spacetime is reviewed. The central problem addressed is
the construction of a perturbative approximation scheme which treats the
initial symmetric state in terms of the field $\phi$, while the state that
emerges at later times is treated in terms of a field $\zeta$, linearly related
to $\phi^2$. The connection between early and late times involves an infinite
sequence of composite propagators. Explicit one-loop calculations are given of
the gap equations that determine quasiparticle masses and of the equation of
motion for $<\phi^2(t)>$ and the renormalization of these equations is
described. The perturbation series needed to describe the symmetric and
broken-symmetry states are not equivalent, and this leads to ambiguities
intrinsic to any perturbative approach. These ambiguities are discussed in
detail and a systematic procedure for matching the two approximations is
described.
