Toward a Precise Measurement of Matter Clustering: Lyα 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 P_F(k), using an improved version of the method of Croft et al. that accounts for the influence of redshift-space distortions, nonlinearity, 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 nongravitational 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 Δz ≈ 25. It has a dimensionless amplitude Δ²(k_p) = 0.74 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 × 10^-3 (km s^-1)^-1 at z = 2.72 (all error bars 1 σ). 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 = 0.16 h Mpc^-1, in good agreement with measurements from the 2dF Galaxy Redshift Survey, and the best-fit normalization is σ₈ = 0.82(Γ/0.15)^-0.44. Matching the observed cluster mass function and our measured Δ²(k_p) in spatially flat cosmological models requires Ω_m = 0.38 + 2.2(Γ - 0.15). Matching Δ²(k_p) in COBE-normalized, flat CDM models with no tensor fluctuations requires Ω_m = (0.29 ± 0.04)n^-2.89 h, 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 length scale 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.