Constraining galaxy formation and cosmology with the conditional luminosity function of galaxies

We use the conditional luminosity function �(L|M)dL, which gives the number of galaxies with luminosities in the range L±dL/2 that reside in a halo of mass M, to link the distribution of galaxies to that of dark matter haloes. Starting from the number density of dark matter haloes predicted by current models of structure formation, we seek the form of �(L|M) that reproduces the galaxy luminosity function and the luminosity dependence of the galaxy clustering strength. We test the models of �(L|M) by comparing the resulting mass-to-light ratios with constraints from the Tully-Fisher (TF) relation and from galaxy clusters. A comparison between model predictions and current observations yields a number of stringent constraints on both galaxy formation and cosmology. In particular, this method can break the degeneracy between 0 and the power-spectrum normalization �8, inherent in current weak-lensing and cluster