Cosmological constraints from a combination of galaxy clustering and lensing - III. Application to SDSS data

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 a 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 cold dark matter (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 7-year Wilkinson Microwave Anisotropy Probe (WMAP7) priors for the spectral index, n, 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 per cent 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.