We investigate the effects of non-Gaussianity in the primordial density field on the reionization history. We rely on a semi-analytic method to describe the processes acting on the intergalactic medium (IGM), relating the distribution of the ionizing sources to that of dark matter haloes. Extending previous work in the literature, we consider models in which the primordial non-Gaussianity is measured by the dimensionless non-linearity parameter f_NL, using the constraints recently obtained from cosmic microwave background data. We predict the ionized fraction and the optical depth at different cosmological epochs assuming two different kinds of non-Gaussianity, characterized by a scale-independent and a scale-dependent f_NL and comparing the results to those for the standard Gaussian scenario. We find that a positive f_NL enhances the formation of high-mass haloes at early epochs, when reionization begins, and, as a consequence, the IGM ionized fraction can grow by a factor up to 5 with respect to the corresponding Gaussian model. The increase of the filling factor has a small impact on the reionization optical depth and is of order ~ 10 per cent if a scale-dependent non-Gaussianity is assumed. Our predictions for non-Gaussian models are in agreement with the latest WMAP results within the error bars, but a higher precision is required to constrain the scale dependence of non-Gaussianity.
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