  We analyze the flux power spectrum and its covariance using simulated Lyman
alpha forests. We find that pseudo-hydro techniques are good approximations of
hydrodynamical simulations at high redshift. However, the pseudo-hydro
techniques fail at low redshift because they are insufficient for
characterizing some components of the low-redshift intergalactic medium,
notably the warm-hot intergalactic medium. Hence, to use the low-redshift Lyman
alpha flux power spectrum to constrain cosmology, one would need realistic
hydrodynamical simulations. By comparing one-dimensional mass statistics with
flux statistics, we show that the nonlinear transform between density and flux
quenches the fluctuations so that the flux power spectrum is much less
sensitive to cosmological parameters than the one-dimensional mass power
spectrum. The covariance of the flux power spectrum is nearly Gaussian. As
such, the uncertainties of the underlying mass power spectrum could still be
large, even though the flux power spectrum can be precisely determined from a
small number of lines of sight.
