  The ordering dynamics of the Higgs field is studied, using techniques
inspired by the study of phase ordering in condensed matter physics, as a first
step to understanding the evolution of cosmic structure through the formation
of topological defects in the early universe. The common feature of these
different physical processes is scaling. A fully analytical approximate scheme
-- the linear-gaussian approach -- is proposed to evaluate 1-point, 2-point,
etc.\ scaling functions for the ordering dynamics of the $O(n)$-symmetric
Higgs-field models.
