Journal or Book Title
We estimate the present-day value of the matter density parameter ΩM 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 ΩM, matching the observed cluster mass function then fixes the value of σ8, 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 ΩM 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 h-1 Mpc, the derived value of ΩM 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 ΩM = 0.46+0.12-0.10 for an open universe and ΩM = 0.34+0.13-0.09 for a flat universe (1 σ errors, not including the uncertainty in cluster normalization). Cluster-normalized models with ΩM = 1 predict too low an amplitude for P(k) at z = 2.5, while models with ΩM = 0.1 predict too high an amplitude. The more general best-fit parameter combination is ΩM + 0.2ΩΛ 0.46 + 1.3(Γ - 0.2), where ΩΛ ≡ Λ/3H20. Analysis of larger, existing samples of QSO spectra could greatly improve the measurement of P(k) from the Lyα forest, allowing a determination of ΩM by this method with a precision of ~15%, limited mainly by uncertainty in the cluster mass function.
Weinberg, DH; Croft, RAC; Hernquist, L; Katz, N; and Pettini, M, "Closing in on Omega(M): The amplitude of mass fluctuations from galaxy clusters and the Ly alpha forest" (1999). ASTROPHYSICAL JOURNAL. 359.