We have performed high-resolution hydrodynamic simulations of the Ly \alpha forest in a variety of popular cold dark matter dominated cosmologies , including a low density and a vacuum-dominated model .
The fluctuation amplitude of these models is chosen to match the observed abundance of galaxy clusters at low redshift .
We assume that the intergalactic medium is photoionized and photoheated by a uniform UV-background with the required amplitude to give the observed mean hydrogen absorption .
We produce simulated spectra , analyze them by fitting Voigt profiles and compare line statistics with those obtained from high resolution observations .
All models give column density distributions in good agreement with observations .
However , the distribution of line widths ( the b -parameter distribution ) reflects differences in the temperature of the intergalactic medium between the models , with colder models producing more narrow lines .
All the models with a low baryon density , \Omega _ { b } h ^ { 2 } = 0.0125 , are too cold to produce a b -parameter distribution in agreement with observations .
Models with a higher baryon density , \Omega _ { b } h ^ { 2 } = 0.025 , are hotter and provide better fits .
Peculiar velocities contribute significantly to the line widths in models with low matter density , and this improves the agreement with observations further .
We briefly discuss alternative mechanisms for reconciling the simulations with the observed b -parameter distributions .