The Linear Theory Power Spectrum from the Lyα Forest in the Sloan Digital Sky Survey

We analyze the SDSS Ly-alpha forest P_F(k,z) measurement to determine thelinear theory power spectrum. Our analysis is based on fully hydrodynamicsimulations, extended using hydro-PM simulations. We account for the effect ofabsorbers with damping wings, which leads to an increase in the slope of thelinear power spectrum. We break the degeneracy between the mean level ofabsorption and the linear power spectrum without significant use of externalconstraints. We infer linear theory power spectrum amplitudeDelta^2_L(k_p=0.009s/km,z_p=3.0)=0.452_{-0.057-0.116}^{+0.069+0.141} and slopen_eff=-2.321_{-0.047-0.102}^{+0.055+0.131} (possible systematic errors areincluded through nuisance parameters in the fit - a factor >~5 smaller errorswould be obtained on both parameters if we ignored modeling uncertainties). Theerrors are correlated and not perfectly Gaussian, so we provide a chi^2 tableto accurately describe the results. The result corresponds to sigma_8=0.85,n=0.94, for a LCDM model with Omega_m=0.3, Omega_b=0.04, and h=0.7, but is mostuseful in a combined fit with the CMB. The inferred curvature of the linearpower spectrum and the evolution of its amplitude and slope with redshift areconsistent with expectations for LCDM models, with the evolution of the slope,in particular, being tightly constrained. We use this information to constrainsystematic contamination, e.g., fluctuations in the UV background. This papershould serve as a starting point for more work to refine the analysis,including technical improvements such as increasing the size and number of thehydrodynamic simulations, and improvements in the treatment of the variousforms of feedback from galaxies and quasars.