  We review recent developments in the theory of the Lyman-alpha 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 Lya
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 Lya absorption in the vicinity of
galaxies, but observations show a Lya deficit within Delta_r ~ 0.5 Mpc/h
(comoving). We investigate idealized models of "winds" and find that they must
eliminate neutral hydrogen out to comoving radii ~1.5 Mpc/h 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 Lya 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.
