Towards a Precise Measurement of Matter Clustering: Lyman-alpha Forest Data at Redshifts 2-4

We measure the filling factor, correlation function, and power spectrum of transmitted flux in a large sample of Lyα forest spectra, comprised of 30 Keck HIRES spectra and 23 Keck LRIS spectra. We infer the linear matter power spectrum P (k) from the flux power spectrum PF (k), using an improved version of the method of Croft et al. (1998) that accounts for the influence of redshift-space distortions, non-linearity, and thermal broadening on the shape of PF (k). The evolution of the shape and amplitude of P (k) over the redshift range of the sample (z ≈ 2−4) is consistent with the predictions of gravitational instability, implying that non-gravitational fluctuations do not make a large contribution to structure in the Lyα forest. Our fiducial measurement of P (k) comes from a subset of the data with 2.3 < z < 2.9, mean absorption redshift 〈z〉 = 2.72, and total path length ∆z ≈ 25. The fiducial P (k) has a dimensionless amplitude ∆(kp) = 0.54 +0.14 −0.12 at wavenumber kp = 0.03(km s )−1; it is well described by a power-law of index ν = −2.47 ± 0.06 or by a CDM-like power spectrum with shape parameter Γ = 9.6 −4.8 × 10(km s)−1 at z = 2.72 (all error bars 1σ). The shape and amplitude of the power spectrum are close to the predictions of leading cosmological models, but different enough to create slight tensions on the values of cosmological parameters when combined with other constraints. For Ωm = 0.4, ΩΛ = 0.6, and inflationary index n = 1, the shape parameter at z = 0 is Γ = 0.12 +0.05 −0.06 h Mpc , somewhat lower than the value inferred from galaxy clustering. Matching the observed cluster mass function and our measured ∆(kp) in flat models with a cosmological constant requires Ωm = 0.50 +0.13 −0.10 for Γ = 0.15, and higher Ωm for larger Γ. A COBE-normalized model with Ωm = 0.4, ΩΛ = 0.6, h = 0.65, Ωbh 2 = 0.02 requires n = 0.85 ± 0.05 in the absence of gravity waves, or n = 0.91 ± 0.03 for a tensor normalization T/S = 7(1 − n). A better determination of the mean opacity of the Lyα forest would increase the precision of our P (k) measurement and remove the main source of systematic uncertainty. Subject headings: Cosmology: observations, quasars: absorption lines, large scale structure of universe