(ABRIDGED)The rise of cosmic structure depends upon the statistical distribution of initial density fluctuations generated by inflation. While the simplest models predict an almost perfectly Gaussian distribution, more-general models predict a level of primordial non-Gaussianity (PNG) that observations might yet be sensitive enough to detect. Recent Planck Collaboration measurements of the CMB temperature anisotropy bispectrum significantly tighten the observational limits, but they are still far from the PNG level predicted by the simplest models of inflation. Probing levels below CMB sensitivities will require other methods, such as searching for the statistical imprint of PNG on galactic halo clustering. During the epoch of reionization (EoR), the first stars and galaxies released radiation into the intergalactic medium (IGM) that created ionized patches whose large-scale geometry and evolution reflected the underlying abundance and large-scale clustering of the star-forming galaxies. This statistical connection between ionized patches in the IGM and galactic halos suggests that observing reionization may be another way to constrain PNG. We employ the linear perturbation theory of reionization and semi-analytic models based on the excursion-set formalism to model the effects of PNG on the EoR. We quantify the effects of PNG on the large-scale structure of reionization by deriving the ionized density bias, i.e. ratio of ionized atomic to total matter overdensities in Fourier space, at small wavenumber. Just as previous studies found that PNG creates a scale-dependent signature in the halo bias, so, too, we find a scale-dependent signature in the ionized density bias. Our results, which differ significantly from previous attempts in the literature to characterize this PNG signature, will be applied elsewhere to predict its observable consequences, e.g. in the cosmic 21cm background.
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