Non‐Gaussianity and the Recovery of the Mass Power Spectrum from the Lyα Forest

Abstract

We investigate the eUect of non-Gaussianity on the reconstruction of the initial mass —eld from the Lya forest. We show that the transmitted —ux of QSO absorption spectra are highly non-Gaussian in terms of the statistics, the kurtosis spectrum, and the scale-scale correlation. These non-Gaussianities cannot be completely removed by the conventional algorithm of Gaussianization, and the scale-scale correlations are largely retained in the mass —eld recovered by the Gaussian mapping. Therefore, the mass power spectrum recovered by the conventional algorithm is systematically lower than the initial mass spectrum on scales at which the local scale-scale correlation is substantial. To reduce the non- Gaussian contamination, we present two methods. The —rst is to perform the Gaussianization scale-by- scale using the discrete wavelet transform (DWT) decomposition. We show that the non-Gaussian features of the Lya forest basically will no longer exist in the scale-by-scale Gaussianized mass —eld. The second method is to choose a proper orthonormal basis (representation) to suppress the eUect of the non-Gaussian correlations. In the quasi-linear regime of cosmic structure formation, the DWT power spectrum is efficient for suppressing the non-Gaussian contamination. These two methods signi—cantly improve the recovery of the mass power spectrum from the Lya forest. Subject headings: cosmology: theorydark matterlarge-scale structure of universe ¨ quasars: absorption lines