Dark Energy Survey year 3 results: Constraints on cosmological parameters and galaxy-bias models from galaxy clustering and galaxy-galaxy lensing using the redMaGiC sample

We constrain cosmological and galaxy-bias parameters using the combination of galaxy clustering and galaxy-galaxy lensing measurements from the Dark Energy Survey Year-3 data. We describe our modeling framework, and choice of scales analyzed, validating their robustness to theoretical uncertainties in small-scale clustering by analyzing simulated data. Using a linear galaxy bias model and redMaGiC galaxy sample, we obtain constraints on the matter density to be $\Omega_{\rm m} = 0.325^{+0.033}_{-0.034}$. We also implement a non-linear galaxy bias model to probe smaller scales that includes parameterization based on hybrid perturbation theory and find that it leads to a 17% gain in cosmological constraining power. We perform robustness tests of our methodology pipeline and demonstrate the stability of the constraints to changes in the theoretical model. Using the redMaGiC galaxy sample as foreground lens galaxies, we find the galaxy clustering and galaxy-galaxy lensing measurements to exhibit significant signals akin to de-correlation between galaxies and mass on large scales, which is not expected in any current models. This likely systematic measurement error biases our constraints on galaxy bias and the $S_8$ parameter. We find that a scale-, redshift- and sky-area-independent phenomenological de-correlation parameter can effectively capture the impact of this systematic error. We trace the source of this de-correlation to a color-dependent photometric issue and minimize its impact on our result by changing the selection criteria of redMaGiC galaxies. Using this new sample, our constraints on the $S_8$ parameter are consistent with previous studies, and we find a small shift in the $\Omega_{\rm m}$ constraints compared to the fiducial redMaGiC sample. We constrain the mean host halo mass of the redMaGiC galaxies in this new sample to be approximately $1.6 \times 10^{13} M_{\odot}/h$.