| We study, in this paper, the non-Gaussian features of the mass density field ofneutral hydrogen fluid and the Lyαtransmitted flux of QSO absorption spectrum fromthe point-of-view of self-similar log-Poisson hierarchy. It has been shown recently that,in the scale range from the onset of nonlinear evolution to dissipation, the velocity andmass density fields of cosmic baryon fluid are extremely well described by the She-Leveque's scaling formula, which is due to the log-Poisson hierarchical cascade. Sincethe mass density ratio between ionized hydrogen to total hydrogen is not uniform inspace, the mass density field of neutral hydrogen component is not given by a similarmapping of total baryon fluid. Nevertheless, we show, with hydrodynamic simulationsamples of the concordanceΛCDM universe, that the mass density field of neutralhydrogen, is also well described by the log-Poisson hierarchy.We then investigate the field of Lyαtransmitted flux of QSO absorption spectrum.Due to redshift distortion, Lyαtransmitted flux fluctuations are no longer to show allfeatures of the log-Poisson hierarchy. However, some non-Gaussian features predictedby the log-Poisson hierarchy are not affected by the redshift distortion. We test thesepredictions with the high resolution and high S/N data of quasars Lyαabsorption spec-tra. All results given by real data, includingβ-hierarchy, high order moments andscale-scale correlation, are found to be well consistent with the log-Poisson hierarchy.We also investigate the non-Gaussian features of the IGM at redshift z～5 fl 6using normalized Lyαtransmitted flux of quasar absorption spectra and cosmologicalhydrodynamic simulation of the concordanceΛCDM universe. We show that the neu-tral hydrogen mass density field and Lyαtransmitted flux fluctuations possess all thenon-Gaussian features predicted by the log-Poisson hierarchy, which depends only ontwo dimensionless parametersβandγ, describing, respectively, the intermittence andsingularity of the random fields. We find that the non-Gaussianity of the Lyαtrans-mitted flux of quasars from z = 4.9 to z = 6.3 can be well reconstructed by the hy-drodynamical simulation samples that assuming a uniform UV background. Although the Gunn-Peterson optical depth and its variance underwent a significant evolution, theintermittency, value ofβ, is almost redshift-independent in the redshift range of 5 - 6.More interesting, compare the result before, we found that the intermittency of quasar'sabsorption spectra on physical scales 0.1-1 h-1Mpc in this redshift range are found tobe the same as that on physical scales 1-10 h-1Mpc at redshifts 2-4. Considering theJeans length is less than 0.1 h-1Mpc at z～5, and 1 h-1Mpc at z～2, all these resultsconsist with the scenario that the nonlinear evolution in high and low redshifts will leadthe cosmic baryon fluid to a state similar to fully developed turbulence yielded by thelog-Poisson hierarchy.We compare the log-Poisson hierarchy with the popular log-normal model of theLyαtransmitted flux. The later is found to yield too strong non-Gaussianity at highorders, while the log-Poisson hierarchy is in agreement with observed data.The log-Poisson non-Gaussianity features generally are sensitive to the inhomogeneity of theUV background. Although the current high redshift data of quasar's spectrum is only ofmoderate-resolution, we find that the non-Gaussian features of the Lyαtransmitted fluxtend to be less in favor of non-uniform UV background in the redshift range considered.
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