Luminosity Density Estimation from Redshift Surveys and the Mass Density of the Universe

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Abstract
In most direct estimates of the mass density (visible or dark) of the universe, a central input parameter is the luminosity density of the universe. Here we consider the measurement of this luminosity density from redshift surveys, as a function of the yet undetermined characteristic scale RH at which the spatial distribution of visible matter tends to a well-defined homogeneity. Making the canonical assumption that the cluster mass-to-luminosity ratio / is the universal one, we can estimate the total mass density as a function Ωm(RH, /). Taking the highest estimated cluster value / ≈ 300 h M☉/L☉ and a conservative lower limit RH 20 h-1 Mpc, we obtain the upper bound Ωm 0.1. We note that, for values of the homogeneity scale RH in the range RH ≈ (90 ± 45) h Mpc, the value of Ωm may be compatible with the nucleosynthesis inferred density in baryons.
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