Our goal in this paper is to test some popular dark matter models by Ly-alphaforest in QSO spectra. Recent observations of the size and velocity of Ly-alphaforest clouds have indicated that the Ly-alpha absorption is probably not givenby collapsed objects, but pre-collapsed regions in the baryonic density field.Therefore, a linear approximation description would be able to provide valuableinformation. We developed a technique to simulate Ly-alpha forest as theabsorption of such pre-collapsed regions under linear approximation regime. Thesimulated Ly-alpha forests in models of the standard cold dark matter (SCDM),the cold plus hot dark matter (CHDM), and the low-density flat cold dark matter(LCDM) have been confronted with observational features, including 1) thenumber density of Ly-alpha lines and its dependencies on redshift andequivalent width; 2) the distribution of equivalent widths and its redshiftdependence; 3) clustering; and 4) the Gunn-Peterson effect. The "standard" CHDMmodel, i.e. 60% cold and 30% hot dark matters and 10\% baryons, is found to bedifficult to pass the Ly-alpha forest test, probably because it producesstructures too late and favors to form structures on large scales instead ofsmall scale objects like Ly-alpha clouds. Within a reasonable range of J_nu,the UV background radiation at high redshift, and delta_th, the threshold ofthe onset of gravitational collapse of the baryonic matter, the LCDM model isconsistent with observational data in all above-mentioned four aspects. Themodel of SCDM can also fit with observation, but it requires a smaller J_nu anda higher delta_th. This suggests that whether a significant part of theLy-alpha forest lines is located in the halos of collapsed objects would becrucial to the success of SCDM.
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