Closing in on Omega(M): The amplitude of mass fluctuations from galaxy clusters and the Ly alpha forest

Abstract

We estimate the present-day value of the matter density parameter Omega(M) by combining constraints from the galaxy cluster mass function with Croft et al.'s recent measurement of the mass power spectrum, P(k), from Ly alpha forest data. The key assumption of the method is that cosmic structure formed by gravitational instability from Gaussian primordial fluctuations. For a specified value of Omega(M), matching the observed cluster mass function then fixes the value of sigma(8), the rms amplitude of mass fluctuations in 8 h(-1) Mpc spheres, and it thus determines the normalization of P(k) at z = 0. The value of Omega(M) also determines the ratio of P(k) at z = 0 to P(k) at z = 2.5, the central redshift of the Ly alpha forest data; the ratio is different for an open universe (Lambda = 0) or a flat universe. Because the Ly alpha forest measurement only reaches comoving scales 2 pi/k similar to 15-20 h-l Mpc, the derived value of Omega(M) depends on the value of the power spectrum shape parameter Gamma, which determines the relative contribution of larger scale modes to sigma(8). Adopting Gamma = 0.2, a value favored by galaxy clustering data, we find Omega(M) = 0.46(-0.10)(+0.12) for an open universe and Omega(M) = 0.34(-0.09)(+0.13) for a flat universe (1 sigma errors, not including the uncertainty in cluster normalization). Cluster-normalized models with Omega(M) = 1 predict too low an amplitude for P(k) at z = 2.5, while models with Omega(M) = 0.1 predict too high an amplitude. The more general best-fit parameter combination is Omega(M) + 0.2 Omega(Lambda) approximate to 0.46 + 1.3(Gamma - 0.2), where Omega(Lambda) equivalent to A/3H(0)(2). Analysis of larger, existing samples of QSO spectra could greatly improve the measurement of P(k) from the Lya forest, allowing a determination of Omega(M) by this method with a precision of similar to 15%, limited mainly by uncertainty in the cluster mass function.