Closing in on Omega_0: The Amplitude of Mass Fluctuations from Galaxy Clusters and the Lyman-alpha Forest

Abstract

We estimate the value of the matter density parameter Ω_0 by combining constraints from the galaxy cluster mass function with Croft et al.'s recent measurement of the mass power spectrum, P(k), from \lya 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 Ω_0, matching the observed cluster mass function then fixes the value of σ_8, the rms amplitude of mass fluctuations in 8\hmpc spheres, and it thus determines the normalization of P(k) at z=0. The value of Ω_0 also determines the ratio of P(k) at z=0 to P(k) at z=2.5, the central redshift of the \lya forest data; the ratio is different for an open universe (Λ=0) or a flat universe. Because the \lya forest measurement only reaches comoving scales 2π/k ~ 15-20\hmpc, the derived value of Ω_0 depends on the value of the power spectrum shape parameter Γ, which determines the relative contribution of larger scale modes to σ_8. Adopting Γ=0.2, a value favored by galaxy clustering data, we find Ω_0 = 0.46^{+0.12}_{-0.10} for an open universe and Ω_0=0.34^{+0.13}_{-0.09} for a flat universe (1σerrors, not including the uncertainty in cluster normalization). Cluster-normalized models with Ω_0=1 predict too low an amplitude for P(k) at z=2.5, while models with Ω_0=0.1 predict too high an amplitude. The more general best fit parameter combination is approximately Ω_0 + 0.2Λ_0 = 0.46 + 1.3(Γ-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 Ω_0 by this method with a precision of ~15%, limited mainly by uncertainty in the cluster mass function.