The ΩM‐ΩΛDependence of the Apparent Cluster Ω

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Abstract
The Canadian Network for Observational Cosmology cluster data are used to constrain the ΩM-ΩΛ pair to the region ΩM 0.24e± 0.3(1-0.4ΩΛ) for 0≤ΩΛ ≤ 1. The constraint is based on estimating the apparent mass density of the universe, Ωe(z), as the product of cluster mass-to-light ratios, M/L, with the field luminosity density at the same redshift. The luminosity density contains a volume element, which for measurements at z > 0 causes Ωe(z) to depend on both the density parameter ΩM and the cosmological constant, ΩΛ. The ΩΛ-dependence of the Ωe(z) measurement is about 25% less than the volume-redshift relation but about 50% greater than the luminosity-redshift relation. Most usefully this constraint is approximately orthogonal to the luminosity-redshift relation in the ΩM-ΩΛ plane. The practical application to measuring cosmological parameters has the considerable benefit that all quantities are used in a differential sense, so that common selection effects and galaxy evolution effects will cancel. The residual differential galaxy evolution between field, and the clustered galaxies can be estimated from the sample data. The inferred ΩM has an inverse correlation with ΩΛ, giving a constraint complementary to both the cosmic microwave background and the supernovae distances. Monte Carlo simulations, calibrated with observational data, show that 100 clusters spread over the 0-1 redshift range, each having M/L values of about 25% accuracy, will measure ΩΛ to about 7% statistical error.