# Emulating galaxy clustering and galaxy-galaxy lensing into the deeply non-linear regime: methodology, information, and forecasts

### Abstract

The combination of galaxy-galaxy lensing (GGL) with galaxy clustering is one of the most promising routes to determining the amplitude of matter clustering at low redshifts. We show that extending clustering+GGL analyses from the linear regime down to $\approx 0.5 h^{-1} \mathrm{Mpc}$ scales increases their constraining power considerably, even after marginalizing over a flexible model of non-linear galaxy bias. Using a grid of cosmological N-body simulations, we construct a Taylor-expansion emulator that predicts the galaxy autocorrelation $\xi_{gg}(r)$ and galaxy-matter cross-correlation $\xi_{gm}(r)$ as a function of $\sigma_8$, $\Omega_m$, and halo occupation distribution (HOD) parameters, which are allowed to vary with large-scale environment to represent possible effects of galaxy assembly bias. We present forecasts for a fiducial case that corresponds to BOSS LOWZ galaxy clustering and SDSS-depth weak lensing (effective source density $\sim 0.3 \mathrm{arcmin}^{-2}$). Using tangential shear and projected correlation function measurements over $0.5 \leq r_p \leq 30 h^{-1} \mathrm{Mpc}$ yields a 2 per cent constraint on the parameter combination $\sigma_8 \Omega_m^{0.6}$, a factor of two better than a constraint that excludes non-linear scales ($r_p > 2 h^{-1} \mathrm{Mpc}, 4 h^{-1} \mathrm{Mpc}$ for $\gamma_t , w_p$). Much of this improvement comes from the non-linear clustering information, which breaks degeneracies among HOD parameters. Increasing the effective source density to $3 \mathrm{arcmin}^{-2}$ sharpens the constraint on $\sigma_8 \Omega_m^{0.6}$ by a further factor of two. With robust modelling into the non-linear regime, low-redshift measurements of matter clustering at the 1-per cent level with clustering+GGL alone are well within reach of current data sets such as those provided by the Dark Energy Survey.

Publication
Monthly Notices of the Royal Astronomical Society, Volume 484, Issue 1, p.989-1006.