Cosmological and astrophysical parameters from the SDSS flux power spectrum and hydrodynamical simulations of the Lyman-alpha forest

(abridged) The flux power spectrum of the Lyman-alpha forest in quasar (QSO) absorption spectra is sensitive to a wide range of cosmological and astrophysical parameters and instrumental effects. Modelling the flux power spectrum in this large parameter space to an accuracy comparable to the statistical uncertainty of large samples of QSO spectra is very challenging. We use here a coarse grid of hydrodynamical simulations run with GADGET-2 to obtain a ``best guess'' model around which we calculate a finer grid of flux power spectra using a Taylor expansion of the flux power spectrum to first order. We find that the SDSS flux power spectrum alone is able to constrain a wide range of parameters including the amplitude of the matter power spectrum sigma_8, the matter density Omega_m, the spectral index of primordial density fluctuations n, the effective optical depth tau_eff and its evolution. The thermal history of the Intergalactic Medium (IGM) is, however, poorly constrained and the SDSS data favour either an unplausibly large temperature or an unplausibly steep temperature-density relation. By enforcing a thermal history of the IGM consistent with that inferred from high-resolution QSO spectra, we find the following values for the best fitting model (assuming a flat Universe with a cosmological constant and zero neutrino mass): Omega_ m=0.28 \pm 0.03, n=0.95\pm0.04, \sigma_8=0.91\pm0.07 (1\sigma error bars).We argue that the major uncertainties in this measurement are still systematic rather than statistical.