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we study, in this paper, the non-Gaussian features of the mass density fieldof neutral hydrogen fluid and the Ly-alpha transmitted flux of QSO absorptionspectrum from the point-of-view of self-similar log-Poisson hierarchy. It hasbeen shown recently that, in the scale range from the onset of nonlinearevolution to dissipation, the velocity and mass density fields of cosmic baryonfluid are extremely well described by the She-Leveque's scaling formula, whichis due to the log-Poisson hierarchical cascade. Since the mass density ratiobetween ionized hydrogen to total hydrogen is not uniform in space, the massdensity field of neutral hydrogen component is not given by a similar mappingof total baryon fluid. Nevertheless, we show, with hydrodynamic simulationsamples of the concordance $\Lambda$CDM universe, that the mass density fieldof neutral hydrogen, is also well described by the log-Poisson hierarchy. Wethen investigate the field of Ly$\alpha$ transmitted flux of QSO absorptionspectrum. Due to redshift distortion, Ly$\alpha$ transmitted flux fluctuationsare no longer to show all features of the log-Poisson hierarchy. However, somenon-Gaussian features predicted by the log-Poisson hierarchy are not affectedby the redshift distortion. We test these predictions with the high resolutionand high S/N data of quasars Ly$\alpha$ absorption spectra. All results givenby real data, including $\beta$-hierarchy, high order moments and scale-scalecorrelation, are found to be well consistent with the log-Poisson hierarchy. Wecompare the log-Poisson hierarchy with the popular log-normal model of theLy$\alpha$ transmitted flux. The later is found to yield too strongnon-Gaussianity at high orders, while the log-Poisson hierarchy is in agreementwith observed data.

Log-Poisson Hierarchical Clustering of Cosmic Neutral Hydrogen and Ly-alpha Transmitted Flux of QSO Absorption Spectrum