Luminosity density estimation from redshift surveys and the mass density of the Universe

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 red-shift surveys, as a function of the yet undetermined characteristic scale R_H 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 M/L is the universal one, we can estimate the total mass density as a function \Omega_m(R_H,M/L). Taking the highest estimated cluster value M/L ~300h and a conservative lower limit R_H > 20 Mpc/h, we obtain the upper bound \Omega_m < 0.1 . We note that for values of the homogeneity scale R_H in the range R_H ~ (90 +/- 45) hMpc, the value of \Omega_m may be compatible with the nucleosynthesis inferred density in baryons.