3.6. Clustering in the inter-galactic medium
It is commonly assumed, based on hydrodynamic simulations, that the neutral hydrogen in the inter-galactic medium (IGM) can be related to the underlying mass distribution. It is then possible to estimate the matter power spectrum on scales of a few megaparsecs from the absorption observed in quasar spectra, the so-called Lyman-alpha forest. The usual procedure is to measure the power spectrum of the transmitted flux, and then to infer the mass power spectrum. Photo-ionization heating by the ultraviolet background radiation and adiabatic cooling by the expansion of the Universe combine to give a simple power-law relation between the gas temperature and the baryon density. It also follows that there is a power-law relation between the optical depth and b. Therefore, the observed flux F = exp(- ) is strongly correlated with b, which itself traces the mass density. The matter and flux power-spectra can be related by
where b(k) is a bias function which is calibrated from simulations. Croft et al.  derived cosmological parameters from Keck Telescope observations of the Lyman-alpha forest at redshifts z = 2 - 4. Their derived power spectrum corresponds to that of a CDM model, which is in good agreement with the 2dF galaxy power spectrum. A recent study using VLT spectra  agrees with the flux power spectrum of Ref. .
This method depends on various assumptions. Seljak et al.  pointed out that errors are sensitive to the range of cosmological parameters explored in the simulations, and the treatment of the mean transmitted flux. Combination of the Lyman-alpha data with WMAP suggested deviation from the scale-invariant n = 1 power spectrum [7, 6], but Seljak et al.  have argued that the combined data set is still compatible with n = 1 model.