We present results from the first high-resolution hydrodynamical simulations of non-Gaussian cosmological models. We focus on the statistical properties of the transmitted Lyman-alpha flux in the high redshift intergalactic medium. Imprints of non-Gaussianity are present and are larger at high redshifts. Differences larger than 20 % at z>3 in the flux probability distribution function for high transmissivity regions (voids) are expected for values of the non linearity parameter f_NL=pm 100 when compared to a standard LCDM cosmology with f_NL=0. We investigate also the one-dimensional flux bispectrum: at the largest scales (corresponding to tens of Mpc) we expect deviations in the flux bispectrum up to 20% at z~4 (for f_NL=pm 100), significantly larger than deviations of ~ 3% in the flux power spectrum. We briefly discuss possible systematic errors that can contaminate the signal. Although challenging, a detection of non-Gaussianities in the interesting regime of scales and redshifts probed by the Lyman-alpha forest, could be possible with future data sets.
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