Non-Gaussian isocurvature perturbations from Goldstone modes generated during inflation

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 ${(H}_{\inf }^2{/M}_{\mathrm{Pl}}^2)\sim {10}^{-6},$ 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.