Non-Gaussianity and the recovery of the mass power spectrum from the Ly alpha forest

We investigate the effect of non-Gaussianity on the reconstruction of the i nitial mass field from the Ly alpha forest. We show that the transmitted fl ux of QSO absorption spectra are highly non-Gaussian in terms of the statis tics, the kurtosis spectrum, and the scale-scale correlation. These non-Gau ssianities cannot be completely removed by the conventional algorithm of Ga ussianization, and the scale-scale correlations are largely retained in the mass held recovered by the Gaussian mapping. Therefore, the mass power spe ctrum recovered by the conventional algorithm is systematically lower than the initial mass spectrum on scales at which the local scale-scale correlat ion is substantial. To reduce the non-Gaussian contamination, we present tw o methods. The first is to perform the Gaussianization scale-by-scale using the discrete wavelet transform (DWT) decomposition. We show that the non-G aussian features of the Ly alpha forest basically will no longer exist in t he scale-by-scale Gaussianized mass held. The second method is to choose a proper orthonormal basis (representation) to suppress the effect of the non -Gaussian correlations. In the quasi-linear regime of cosmic structure form ation, the DWT power spectrum is efficient for suppressing the non-Gaussian contamination. These two methods significantly improve the recovery of the mass power spectrum from the Lya alpha forest.