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 P F (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 P F (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. It has a dimensionless amplitude ∆ 2 (k p ) = 0.74 +0.20 −0.16 at wavenumber k p = 0.03(km s −1 ) −1 and is well described by a power-law of index ν = −2.43±0.06 or by a CDM-like power spectrum with shape parameter Γ ′ = 1.3 +0.7 −0.5 ×10 −3 (km s −1 ) −1 at z = 2.72 (all error bars 1σ). The correspondence to present day P (k) parameters depends on the adopted cosmology. For Ω m = 0.4, Ω Λ = 0.6, the best-fit shape parameter is Γ = 0.16h Mpc −1 , in good agreement with measurements from the 2dF Galaxy Redshift Survey, and the best-fit normalization is σ 8 = 0.82(Γ/0.15) −0.44 . Matching the observed cluster mass function and our measured ∆ 2 (k p ) in spatially flat cosmological models requires Ω m = 0.38 +0.10 −0.08 + 2.2(Γ − 0.15). Matching ∆ 2 (k p ) in COBEnormalized, flat CDM models with no tensor fluctuations requires Ω m = (0.29 ± 0.04)n −2.89 h −1.9 65 , and models that satisfy this constraint are also consistent with our measured logarithmic slope. The Lyα forest complements other observational probes of the linear matter power spectrum by constraining a regime of redshift and lengthscale not accessible by other means, and the consistency of these inferred parameters with independent estimates provides further support for a cosmological model based on inflation, cold dark matter, and vacuum energy.

We report the detection of deuterium absorption at redshift 2.525659 toward Q1243+3047. We describe improved methods to estimate the deuterium to hydrogen abundance ratio (D/H) in absorption systems, including improved modeling of the continuum level, the Ly forest, and the velocity structure of the absorption. Together with improved relative flux calibration, these methods give D=H ¼ 2:42 À0:38 Â 10 À5 , from the log D/H-values toward five QSOs. The dispersion in the five values is larger than we expect from their individual measurement errors, and we suspect this is because some of these errors were underestimated. We observe a trend in D/H with log N H i that we also suspect is spurious. The best value for D/H is 0.6 smaller than we quoted in O'Meara et al. from three QSOs, and although we have more values, the error is similar because the dispersion is larger. In standard big bang nucleosynthesis (SBBN), the best D/H corresponds to a baryon-to-photon ratio ¼ 5:9 AE 0:5 Â 10 À10 and gives precise predictions for the primordial abundances of the other light nuclei. We predict more 4 He than is reported in most measurements, although not more than allowed by some estimates of the systematic errors. We predict a 3 He abundance very similar to that reported by Bania et al., and we predict 3-4 times more 7 Li than is seen in halo stars. It is unclear if those stars could have destroyed this much of their 7 Li. The -value from D/H corresponds to a cosmological baryon density b h 2 ¼ 0:0214 AE 0:0020 (AE9.3%), which agrees with the WMAP value of b h 2 ¼ 0:0224 AE 0:001.