We examine the dependence of the mass-to-light ( M / L ) ratio of large-scale structure on cosmological parameters , in models that are constrained to match observations of the projected galaxy correlation function w _ { p } ( r _ { p } ) and the galaxy luminosity function .
For a sequence of cosmological models with a fixed , observationally motivated power spectrum shape and increasing normalization \sigma _ { 8 } , we find parameters of the galaxy halo occupation distribution ( HOD ) that reproduce w _ { p } ( r _ { p } ) measurements as a function of luminosity from the Sloan Digital Sky Survey ( SDSS ) .
From these HOD models we calculate the r -band conditional luminosity function \Phi ( L|M _ { h } ) , and from this the mean M / L ratio as a function of halo mass M _ { h } .
We also use \Phi ( L|M _ { h } ) to populate halos of N-body simulations with galaxies and thereby compute M / L in a range of large-scale environments , including cluster infall regions .
For all cosmological models , the M / L ratio in high mass halos or high density regions is approximately independent of halo mass or smoothing scale .
However , the “ plateau ” value of M / L depends on \sigma _ { 8 } in addition to the obvious proportionality with the matter density parameter \Omega _ { m } , and it represents the universal value \langle M / L \rangle = \Omega _ { m } \rho _ { \mbox { \scriptsize crit } } / \rho _ { \mbox { \scriptsize lum } } only for models in which the galaxy correlation function is approximately unbiased , i.e. , with \sigma _ { 8 } \approx \sigma _ { 8 } { { } _ { g } } .
Our results for cluster mass halos follow the trend ( M / L ) _ { cl } = 577 ( \Omega _ { m } / 0.3 ) ( \sigma _ { 8 } / 0.9 ) ^ { 1.7 } h M _ { \odot } / L _ { \odot } .
Combined with Carlberg et al. ’ s ( 1996 ) mean M / L ratio for CNOC galaxy clusters , this relation implies ( \sigma _ { 8 } / 0.9 ) ( \Omega _ { m } / 0.3 ) ^ { 0.6 } = 0.75 \pm 0.06 . M / L estimates for SDSS clusters and the virial regions of clusters in the CAIRNS survey imply a similar value of \sigma _ { 8 } \Omega _ { m } ^ { 0.6 } , while the CAIRNS estimates for cluster infall regions imply a lower value .
These results are inconsistent with parameter values \Omega _ { m } \approx 0.3 , \sigma _ { 8 } \approx 0.9 favored by recent joint analyses of cosmic microwave background measurements and other large scale structure data , though they agree with values inferred from van den Bosch et al. ’ s ( 2003 ) analysis of the 2dF Galaxy Redshift Survey .
We discuss possible resolutions of this discrepancy , none of which seems entirely satisfactory .
In appendices we present an improved formula for halo bias factors calibrated on our 360 ^ { 3 } N-body simulations and an improved analytic technique for calculating the galaxy correlation function from a given cosmological model and HOD .