Cosmological constraints from the masses and abundances of L∗ galaxies

We place limits on the mean density of the universe Ωm and the effective slope of the linear power spectrum around a megaparsec scale neff by comparing the universal mass function to the observed luminosity function. Numerical simulations suggest that the dark matter halo mass function at small scales depends only on Ωm(neff +3) independent of the overall power spectrum normalization. Matching the halo abundance to the observed luminosity function requires knowing the relation between the virial mass and luminosity (separately for early and late type galaxies) and the fraction of galaxies that reside in larger halos such as groups and clusters, all of which can be extracted from the galaxy-galaxy lensing. We apply the recently derived values from SDSS and find Ωm(neff +3) = (0.15± 0.05)/(1− fdh), where fdh accounts for the possibility that some fraction of halos may be dark or without bright central galaxy. A model with Ωm = 0.25 and primordial n = 0.8 or with Ωm = 0.2 and n = 1 agrees well with these constraints even in the absence of dark halos, although with the current data somewhat higher values for Ωm and n are also acceptable.