We simultaneously constrain cosmology and galaxy bias using measurements of galaxy abundances , galaxy clustering and galaxy-galaxy lensing taken from the Sloan Digital Sky Survey .
We use the conditional luminosity function ( which describes the halo occupation statistics as function of galaxy luminosity ) combined with the halo model ( which describes the non-linear matter field in terms of its halo building blocks ) to describe the galaxy-dark matter connection .
We explicitly account for residual redshift space distortions in the projected galaxy-galaxy correlation functions , and marginalize over uncertainties in the scale dependence of the halo bias and the detailed structure of dark matter haloes .
Under the assumption of a spatially flat , vanilla \Lambda CDM cosmology , we focus on constraining the matter density , \Omega _ { m } , and the normalization of the matter power spectrum , \sigma _ { 8 } , and we adopt WMAP7 priors for the spectral index , n _ { s } , the Hubble parameter , h , and the baryon density , \Omega _ { b } .
We obtain that \Omega _ { m } = 0.278 _ { -0.026 } ^ { +0.023 } and \sigma _ { 8 } = 0.763 _ { -0.049 } ^ { +0.064 } ( 95 % CL ) .
These results are robust to uncertainties in the radial number density distribution of satellite galaxies , while allowing for non-Poisson satellite occupation distributions results in a slightly lower value for \sigma _ { 8 } ( 0.744 _ { -0.047 } ^ { +0.056 } ) .
These constraints are in excellent agreement ( at the 1 \sigma level ) with the cosmic microwave background constraints from WMAP .
This demonstrates that the use of a realistic and accurate model for galaxy bias , down to the smallest non-linear scales currently observed in galaxy surveys , leads to results perfectly consistent with the vanilla \Lambda CDM cosmology .