Toward a Precise Measurement of Matter Clustering: Lyα Forest Data at Redshifts 2–4

We measure the filling factor, correlation function, and power spectrum oftransmitted flux in a large sample of Lya forest spectra, comprised of 30 KeckHIRES spectra and 23 Keck LRIS spectra. We infer the linear matter powerspectrum P(k) from the flux power spectrum P_F(k), using an improved version ofthe method of Croft et al. (1998) that accounts for the influence of z-spacedistortions, non- linearity, and thermal broadening on P_F(k). The evolution ofthe shape and amplitude of P(k) over the range z= 2-4 is consistent withgravitational instability, implying that non-gravitational fluctuations do notmake a large contribution. Our fiducial measurement of P(k) comes from datawith = 2.72. It has amplitude Delta^2(k_p)=0.74^0.20_-0.16 at wavenumberk_p=0.03 (km/s)^-1 and is well described by a power-law of index -2.43 +/- 0.06or by a CDM-like power spectrum with shape parameter Gamma'=1.3^+0.7_-0.5*10^-3(km/s) at z=2.72. For Omega_m=0.4, Omega_Lam=0.6, the best-fit Gamma =0.16(h^-1mpc)^-1, in good agreement with the 2dF Galaxy Redshift Survey, and thebest-fit sigma_8=0.82 (Gamma/0.15)^-0.44. Matching the observed cluster massfunction and our Delta^2(k_p) in spatially flat models requiresOmega_m=0.38^+0.10_-0.08 + 2.2 (Gamma-0.15). Matching Delta^2(k_p) inCOBE-normalized, flat CDM models with no tensor fluctuations requires Omega_m =(0.29 +/-0.04) n^-2.89 h_65^-1.9. The Lya forest complements other probes ofP(k) by constraining a regime of redshift and lengthscale not accessible byother means, and the consistency of these inferred parameters with independentestimates provides further support for inflation, cold dark matter, and vacuumenergy (abridged).Comment: Revised version fixes error in normalization (now 1 sigma higher). ApJ in press Dec 10 issue, 34 pages, 23 postscript figures, emulateapj.st