  Numerical hydrodynamical simulations are used to predict the expected
absorption properties of the Lyman-Alpha forest for a variety of Cold Dark
Matter dominated cosmological scenarios: CHDM, OCDM, LCDM, SCDM, and tCDM.
Synthetic spectra are constructed duplicating the resolution, signal-to-noise
ratio, and wavelength coverage of several published high resolution spectra,
and their statistical properties compared on the basis of the flux distribution
of the spectra, the distribution of coefficients in a wavelet decomposition of
the spectra, and the distributions of absorption line profile parameters.
Agreement between the measured and predicted cumulative distributions is found
at the few to several percent level. The best-fitting models to the flux
distribution correspond to normalizations on the scale of the cosmological
Jeans length of 1.3 < sigma_J < 1.7 at z=3. No single model provides an
acceptable match to all the distributions. Larger median Doppler parameters are
found in the measured spectra than predicted by all but the lowest
normalization models (CHDM and tCDM), which provide poor fits to the flux
distributions. The discrepancy in Doppler parameters is particularly large for
absorption systems optically thin at the Lyman-Alpha line-centre. This may
indicate the need to introduce additional energy injection throughout the IGM,
as may be provided by late HeII reionization (z_HeII~3.5) or supernovae-driven
winds from young galaxies. The models require a hydrogen ionization rate at
redshifts 1.7<z<3.5 within a factor of 2 of that predicted from QSOs alone as
the sources of the UV photoionization background, although with a slower rate
of decline with redshift at z>3.5 than predicted from current QSO counts.
