Closing in on Ω0: the Amplitude of Mass Fluctuations from Galaxy Clusters and the Lyman-alpha Forest

We estimate the value of the matter density parameter Ω0 by combining constraints from the galaxy cluster mass function with Croft et al.’s recent measurement of the mass power spectrum, P (k), from Lyα 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 Ω0, matching the observed cluster mass function then fixes the value of σ8, the rms amplitude of mass fluctuations in 8 h Mpc spheres, and it thus determines the normalization of P (k) at z = 0. The value of Ω0 also determines the ratio of P (k) at z = 0 to P (k) at z = 2.5, the central redshift of the Lyα forest data; the ratio is different for an open universe (Λ = 0) or a flat universe. Because the Lyα forest measurement only reaches comoving scales 2π/k ∼ 15 − 20 hMpc, the derived value of Ω0 depends on the value of the power spectrum shape parameter Γ, which determines the relative contribution of larger scale modes to σ8. Adopting Γ = 0.2, a value favored by galaxy clustering data, we find Ω0 = 0.46 +0.12 −0.10 for an open universe and Ω0 = 0.34 +0.13 −0.09 for a flat universe (1σ errors, not including the uncertainty in cluster normalization). Cluster-normalized models with Ω0 = 1 predict too low an amplitude for P (k) at z = 2.5, while models with Ω0 = 0.1 predict too high an amplitude. The more general best fit parameter combination is Ω0+0.2λ0 ≈ 0.46+1.3(Γ−0.2), where λ0 ≡ Λ/3H 2 0 . Analysis of larger, existing samples of QSO spectra could greatly improve the measurement of P (k) from the Lyα forest, allowing a determination of Ω0 by this method with a precision of ∼ 15%, limited mainly by uncertainty in the cluster mass function. Subject headings: cosmology: observations, cosmology: theory, large-scale structure of universe