Inferring the dark matter power spectrum from the Lyman-alpha forest in high-resolution QSO absorption spectra

We use the LUQAS sample (Kim et al. 2004), a set of 27 high-resolution and high signal-to-noise QSO absorption spectra at a median redshift of z=2.25, and the data from Croft et al. (2002) at a median redshift of z=2.72, together with a large suite of high-resolution large box-size hydro-dynamical simulations, to estimate the linear dark matter power spectrum on scales 0.003 s/km < k <0.03 s/km. Our re-analysis of the Croft et al. data agrees well with their results if we assume the same mean optical depth and gas temperature-density relation. The inferred linear dark matter power spectrum at z=2.72 also agrees with that inferred from LUQAS at lower redshift if we assume that the increase of the amplitude is due to gravitational growth between these redshifts. We further argue that the smaller mean optical depth measured from high-resolution spectra is more accurate than the larger value obtained from low-resolution spectra by Press et al. (1993) which Croft et al. used. For the smaller optical depth we obtain a ~ 20% higher value for the rms fluctuation amplitude of the matter density. By combining the amplitude of the matter power spectrum inferred from the Lyman-alpha forest with the amplitude on large scales inferred from measurements of the CMB we obtain constraints on the primordial spectral index n and the normalisation sigma_8. For values of the mean optical depth favoured by high-resolution spectra, the inferred linear power spectrum is consistent with a LambdaCDM model with a scale-free (n=1) primordial power spectrum.