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The combination of galaxy-galaxy lensing (GGL) and galaxy clustering is apowerful probe of low redshift matter clustering, especially if it is extendedto the non-linear regime. To this end, we extend the N-body and halo occupationdistribution (HOD) emulator method of arxiv:1907.06293 to model the redMaGiCsample of colour-selected passive galaxies in the Dark Energy Survey (DES),adding parameters that describe central galaxy incompleteness, galaxy assemblybias, and a scale-independent multiplicative lensing bias $A_{lens}$. We usethis emulator to forecast cosmological constraints attainable from the GGLsurface density profile $\Delta\Sigma(r_p)$ and the projected galaxycorrelation function $w_{p,gg}(r_p)$ in the final (Year 6) DES data set overscales $r_p=0.3-30h^{-1}$ Mpc. For a $3\%$ prior on $A_{lens}$ we forecastprecisions of $1.9\%$, $2.0\%$, and $1.9\%$ on $\Omega_m$, $\sigma_8$, and $S_8\equiv \sigma_8\Omega_m^{0.5}$, marginalized over all halo occupationdistribution (HOD) parameters as well as $A_{lens}$ and a point-masscontribution to $\Delta\Sigma$. Adding scales $r_p=0.3-3h^{-1}$ Mpc improvesthe $S_8$ precision by a factor of $\sim1.6$ relative to a large scale($3.0-30.0h^{-1}$ Mpc) analysis, equivalent to increasing the survey area by afactor of ${\sim}2.6$. Sharpening the $A_{lens}$ prior to $1\%$ furtherimproves the $S_8$ precision by a factor of $1.7$ (to $1.1\%$), and itamplifies the gain from including non-linear scales. Our emulator achievespercent-level accuracy similar to the projected DES statistical uncertainties,demonstrating the feasibility of a fully non-linear analysis. Obtaining preciseparameter constraints from multiple galaxy types and from measurements thatspan linear and non-linear clustering offers many opportunities for internalcross-checks, which can diagnose systematics and demonstrate the robustness ofcosmological results.

Exploiting Non-linear Scales in Galaxy-Galaxy Lensing and Galaxy Clustering: A Forecast for the Dark Energy Survey