Matter power spectrum from the Lyman-alpha forest: myth or reality?

We investigate possible systematic errors in the recent measurement of the matter power spectrum from the Lyman-alpha forest by Croft et al. We find that for a large set of prior cosmological models the Croft et al. result holds quite well, with systematic errors being comparable with random ones, when a dependence of the recovered-matter power spectrum on the cosmological parameters at z similar to3 is taken into account. We find that peculiar velocities cause the flux power spectrum to be smoothed over about 100-300 km s(-1), depending on scale. Consequently, the recovered-matter power spectrum is a smoothed version of the underlying true power spectrum. Uncertainties in the recovered power spectrum are thus correlated over about 100-300 km s(-1). As a side effect, we find that residual fluctuations in the ionizing background, while having almost no effect on the recovered-matter power spectrum, significantly bias estimates of the baryon density from the Lyman-alpha forest data. We therefore conclude that the Croft et al. result provides a powerful new constraint on cosmological parameters and models of structure formation.