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 .
In this way , we investigate how the interplay between astrophysical and cosmological parameters affects their measurements using the recently published flux power spectrum obtained from 3035 SDSS QSOs ( McDonald et al .
2004 ) .
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 \pm 0.04 , \sigma _ { 8 } = 0.91 \pm 0.07 ( 1 \sigma error bars ) .
The values for \sigma _ { 8 } and n are consistent with those obtained by McDonald et al .
with different simulations for similar assumptions .
We argue , however , that the major uncertainties in this measurement are still systematic rather than statistical .