2002ApJ...581...20C

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^+0.20_–0.16at 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_–0.5x10^–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^+0.10_–0.08+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^–1.9₆₅, 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.