  We investigate non-Gaussian isocurvature perturbations generated by the
evolution of Goldstone modes during inflation. If a global symmetry is broken
``before'' inflation, the resulting Goldstone modes are disordered during
inflation in a precise and predictable way. After inflation these Goldstone
modes order themselves in a self-similar way, much as Goldstone modes in field
ordering scenarios based on the Kibble mechanism. For $(H_{inf}^2/M_{pl}^2)\sim
10^{-6},$ through their gravitational interaction these Goldstone modes
generate density perturbations of approximately the right magnitude to explain
the cosmic microwave background (CMB) anisotropy and seed the structure seen in
the universe today. We point out that for the pattern of symmetry breaking in
which a global $U(1)$ is completely broken, the inflationary evolution of the
Goldstone field may be treated as that of a massless scalar field. Unlike the
more commonly discussed case in which a global $U(1)$ is completely broken in a
cosmological phase transition, in the inflationary case the production of
defects can be made exponentially small, so that Goldstone field evolution is
completely linear. In such a model non-Gaussian perturbations result because to
lowest order density perturbations are sourced by products of Gaussian fields.
Consequently, in this non-Gaussian model N-point correlations may be calculated
by evaluating Feynman diagrams. We explore the issue of phase dispersion and
conclude that this non-Gaussian model predicts Doppler peaks in the CMB
anisotropy.
