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

(1.18)

where b(k) is a bias function which is calibrated from simulations. Croft et al. [33] 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 [34] agrees with the flux power spectrum of Ref. [33].

This method depends on various assumptions. Seljak et al. [35] 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. [35] have argued that the combined data set is still compatible with n = 1 model.