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Non-Gaussianity from Self-Ordering Scalar Fields
While a nearly scale-invariant spectrum of primordial adiabatic perturbations is consistent with
current cosmological data, there is still room for primordial isocurvature perturbations that con-
tribute roughly 10% to the power spectrum. Self-ordering scalar ?elds provide a simple but elegant
mechanism for producing a scale-invariant spectrum of such perturbations, but these perturbations
will be highly non-Gaussian. Here we calculate the bispectrum that arises in these models. We
?nd a compact analytic expression for the bispectrum, evaluate it numerically, and provide a simple
approximation that may be useful for data analysis. The bispectrum is largest for triangles that
are aligned (have edges k1 = 2k2 = 2k3 ) as opposed to the local-model bispectrum, which peaks for
squeezed triangles (k1 = k2 >> k3 ) and the equilateral bispectrum, which peaks at k1 = k2 = k3.
We estimate that this non-Gaussianity should be easily detectable by the Planck satellite if the
contribution from self-ordering scalar ?elds to primordial perturbations is near the current upper
limit.
