  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.
