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 the linear theory power spectrum. Our analysis is based on fully hydrodynamic simulations, extended using hydro-particle-mesh simulations. We account for the effect of absorbers with damping wings, which leads to an increase in the slope of the linear power spectrum. We break the degeneracy between the mean level of absorption and the linear power spectrum without significant use of external constraints. We infer linear theory power spectrum amplitude Delta(L)(2)(k(p) = 0.009 s km(-1); z(p) = 3.0) 0: 452(-0.057 -0.116)(+0.069 +0.141) and slope n(eff) (k(p), z(p)) = -2.321(-0.047 -0.102)(+0.055 +0.131) (possible systematic errors are included through nuisance parameters in the fit: a factor greater than or similar to 5 smaller errors would be obtained on both parameters if we ignored modeling uncertainties). The errors are correlated and not perfectly Gaussian, so we provide a chi 2 table to accurately describe the results. The result corresponds to sigma(8) = 0.85, n = 0.94 for a Lambda CDM model with Omega(m) = 0.3, Omega(b) = 0.04, and h = 0.7 but is most useful in a combined fit with the CMB. The inferred curvature of the linear power spectrum and the evolution of its amplitude and slope with redshift are consistent with expectations for Lambda CDM models, with the evolution of the slope, in particular, being tightly constrained. We use this information to constrain systematic contamination, e. g., fluctuations in the UV background. This paper should serve as a starting point for more work to refine the analysis, including technical improvements such as increasing the size and number of the hydrodynamic simulations and improvements in the treatment of the various forms of feedback from galaxies and quasars.