Abstract. We review recent developments in the theory of the Lyα forest and their implications for the role of the forest as a test of cosmological models. Simulations predict a relatively tight correlation between the local Lyα optical depth and the local gas or dark matter density. Statistical properties of the transmitted flux can constrain the amplitude and shape of the matter power spectrum at high redshift, test the assumption of Gaussian initial conditions, and probe the evolution of dark energy by measuring the Hubble parameter H(z). Simulations predict increased Lyα absorption in the vicinity of galaxies, but observations show a Lyα deficit within ∆ r ∼ 0.5h −1 Mpc (comoving). We investigate idealized models of "winds" and find that they must eliminate neutral hydrogen out to comoving radii ∼ 1.5h −1 Mpc to marginally explain the data. Winds of this magnitude suppress the flux power spectrum by ∼ 0.1 dex but have little effect on the distribution function or threshold crossing frequency. In light of the stringent demands on winds, we consider the alternative possibility that extended Lyα emission from target galaxies replaces absorbed flux, but we conclude that this explanation is unlikely. Taking full advantage of the data coming from large telescopes and from the Sloan Digital Sky Survey will require more complete understanding of the galaxy proximity effect, careful attention to continuum determination, and more accurate numerical predictions, with the goal of reaching 5 − 10% precision on key cosmological quantities.
PHYSICS OF THE FORESTThe 1990s saw four epochal advances in our understanding of the Lyα forest. Spectra of quasar pairs showed coherence over scales of a hundred kpc and more, implying large sizes and thus low densities for the absorbing structures [1,2,3,4]. Keck HIRES spectra of unprecedented resolution and signal-to-noise demonstrated the ubiquity of weakly fluctuating Lyα absorption in the high redshift universe [5], and they revealed the presence of metal lines associated with low column density hydrogen absorbers [6,7]. Finally, and most directly relevant to this review, a combination of numerical simulations and related analytic models led to a compelling new physical picture of Lyα forest absorption [8,9,10,11,12,13,14,15].The basic numerical result is simple to summarize: given a cosmological scenario motivated by independent observations, 3-d simulations that incorporate gravity, gas dynamics, and photoionization by the UV background produce something very much like the observed Lyα forest, an outcome that requires no ad hoc adjustments to the model. The top three rows of Figure 1 illustrate this point, showing, respectively, the observed Lyα forest of the z = 3.62 quasar Q1422+231, expanded views of four selected regions of this spectrum, and simulated spectra of the same length along four randomly selected lines of sight through a cosmological simulation. The simulation uses smoothed