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. (2001). We find that for a large set of prior cosmological models the Croft et al. result holds quite well, with systematic errors being comparable to random ones, when a dependence of the recovered matter power spectrum on the cosmological parameters at z~3 is taken into account. We find that peculiar velocities cause the flux power spectrum to be smoothed over about 100-300 km/s, dependng 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. 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.