Cosmology with Stacked Cluster Weak Lensing and Cluster-Galaxy Cross-Correlations

Cluster weak lensing is a sensitive probe of cosmology, particularly the amplitude of matter clustering sigma(8) and matter density parameter Omega(m). The main nuisance parameter in a cluster weak lensing cosmological analysis is the scatter between the true halo mass and the relevant cluster observable, denoted sigma(lnMc). We show that combining the cluster weak lensing observable Delta Sigma with the projected cluster-galaxy cross-correlation function w(p,cg) and galaxy autocorrelation function w(p,g)g can break the degeneracy between sigma(8) and s(lnMc) to achieve tight, per cent-level constraints on sigma(8). Using a grid of cosmological N-body simulations, we compute derivatives of Delta Sigma, w(p,cg), and w(p,gg) with respect to sigma(8), Omega(m), sigma(lnMc), and halo occupation distribution (HOD) parameters describing the galaxy population. We also compute covariance matrices motivated by the properties of the Dark Energy Survey cluster and weak lensing survey and the BOSS CMASS galaxy redshift survey. For our fiducial scenario combining Delta Sigma, w(p,cg), and w(p,gg) measured over 0.3-30.0 h(-1) Mpc, for clusters at z = 0.35-0.55 above a mass threshold M-c approximate to 2 x 10(14) h(-1) M-circle dot, we forecast a 1.4 per cent constraint on sigma(8) while marginalizing over sigma(lnMc) and all HOD parameters. Reducing the mass threshold to 1 x 10(14) h(-1) M-circle dot and adding a z = 0.15-0.35 redshift bin sharpens this constraint to 0.8 per cent. The small-scale (r(p) < 3.0 h(-1) Mpc) 'mass function' and large-scale (r(p) > 3.0 h(-1) Mpc) 'halo-mass cross-correlation' regimes of Delta Sigma have comparable constraining power, allowing internal consistency tests from such an analysis.