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 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, the Hubble parameter, and the
baryon density. We obtain that \Omegam = 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.
