Emulating galaxy clustering and galaxy-galaxy lensing into the deeply nonlinear 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 $\sim 0.5h^{-1}$ 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 ${\xi }_{\text{gg}}(r)$ and galaxy-matter cross-correlation ${\xi }_{\text{gm}}(r)$ 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 $\sim 0.3$ arcmin${}^{-2}$). Using tangential shear and projected correlation function measurements over $0.5\le r_p\le 30h^{-1}$ Mpc yields a 1.8% constraint on the parameter combination ${\sigma }_8{\Omega }_m^{0.58}$, a factor of two better than a constraint that excludes non-linear scales ($r_p>2h^{-1}$ Mpc, $4h^{-1}$ Mpc for ${\gamma }_t,w_p$). Much of this improvement comes from the non-linear clustering information, which breaks degeneracies among HOD parameters that would otherwise degrade the inference of matter clustering from GGL. Increasing the effective source density to $3$ arcmin${}^{-2}$ sharpens the constraint on ${\sigma }_8{\Omega }_m^{0.58}$ by a further factor of two. With robust modeling into the non-linear regime, low-redshift measurements of matter clustering at the 1-percent level with clustering+GGL alone are well within reach of current data sets such as those provided by the Dark Energy Survey.

arXiv comment23 pages, 7 figures

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