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 Lyalpha 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 (zapproximate to2-4) is consistent with the predictions of gravitational instability, implying that non-gravitational fluctuations do not make a large contribution to structure in the Lyalpha forest. Our fiducial measurement of P(k) comes from a subset of the data with 2.3<2.9, mean absorption redshift =2.72, and total path length Deltazapproximate to25. It has a dimensionless amplitude Delta(2)(k(p))=0.74(-0.16)(+0.20) at wavelength number k(p)=0.03 (km s(-1))(-1) and is well described by a power law of index nu=-2.43+/-0.06 or by a CDM-like power spectrum with shape parameter Gamma'=1.3(0.5)(0.7)x10(-3) (km s(-1))(-1) at z=2.72 (all error bars 1 sigma). The correspondence to present-day P(k) parameters depends on the adopted cosmology. For Omega(m)=0.4, Omega(Lambda)=0.6, the best-fit shape parameter is Gamma=0.16 h Mpc(-1), in good agreement with measurements from the 2dF Galaxy Redshift Survey, and the best-fit normalization is sigma(8)=0.82(Gamma/0.15)(-0.44). Matching the observed cluster mass function and our measured Delta(2) (k(p)) in spatially at cosmological models requires Omega(m)=0.38(-0.08)(+0.10) + 2.2(Gamma-0.15). Matching Delta(2) (k(p)) in COBE-normalized, at CDM models with no tensor fluctuations requires Omega(m)=(0.29+/-0.04)n(-2.89) h(65)(-1.9), and models that satisfy this constraint are also consistent with our measured logarithmic slope. The Lyalpha 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.