  Evolution of the order parameter in condensed matter analogues of
cosmological phase transitions is discussed. It is shown that the density of
the frozen-out topological defects is set by the competition between the quench
rate -- the rate at which the phase transition is taking place -- and the
relaxation rate of the order parameter. More specifically, the characteristic
domain size which determines the typical distance separating topological
defects in the new broken symmetry phase (and, therefore, their density) is
determined by the correlation length at the instant at which the relaxation
timescale of the order parameter is equal to the time from the phase
transition. This scenario shares with the Kibble mechanism the idea that
topological defects will appear ``in between'' domains with independently
chosen broken symmetry vacuum. However, it differs from the original proposal
in estimating the size of such domains through the non-equilibrium aspects of
the transition (quench rate), rather than through the Ginzburg temperature at
which thermally activated symmetry restoration can still occur in the
correlation - length sized volumes of the broken symmetry phase. This scenario
can be employed to analyze recent superfluid quench experiments carried out in
bulk He$^4$ to study the analogue of the ``cosmological'' prediction of
significant vortex line production. It can be also applied to superfluid
quenches in annular geometry, as well as to the rapid phase transition from the
normal metal to superconductor, where the symmetry breaking occurs in the order
parameter with the local (rather than a global) gauge. Cosmological
implications of the revised defect formation scenario with the critical domain
size set by the freeze-out time rather than by the Ginzburg temperature are
also briefly considered.
