Cosmological constraints from galaxy-lensing cross correlations using BOSS galaxies with SDSS and CMB lensing

We present cosmological parameter constraints based on a joint modeling of galaxy-lensing cross correlations and galaxy clustering measurements in the SDSS, marginalizing over small-scale modeling uncertainties using mock galaxy catalogs, without explicit modeling of galaxy bias. We show that our modeling method is robust to the impact of different choices for how galaxies occupy dark matter halos and to the impact of baryonic physics (at the $\sim2\%$ level in cosmological parameters) and test for the impact of covariance on the likelihood analysis and of the survey window function on the theory computations. Applying our results to the measurements using galaxy samples from BOSS and lensing measurements using shear from SDSS galaxies and CMB lensing from Planck, with conservative scale cuts, we obtain $S_8\equiv\left(\frac{\sigma_8}{0.8228}\right)^{0.8}\left(\frac{\Omega_m}{0.307}\right)^{0.6}=0.85\pm0.05$ (stat.) using LOWZ $\times$ SDSS galaxy lensing, and $S_8=0.91\pm0.1$ (stat.) using combination of LOWZ and CMASS $\times$ Planck CMB lensing. We estimate the systematic uncertainty in the galaxy-galaxy lensing measurements to be $\sim6\%$ (dominated by photometric redshift uncertainties) and in the galaxy-CMB lensing measurements to be $\sim3\%$, from small scale modeling uncertainties including baryonic physics.