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 σ₈ and matter density parameter Ω_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 σ _{ln M_ c}. We show that combining the cluster weak lensing observable ΔΣ with the projected cluster-galaxy cross-correlation function w_p,cg and galaxy autocorrelation function w_p,gg can break the degeneracy between σ₈ and σ _{ln M_ c} to achieve tight, per cent-level constraints on σ₈. Using a grid of cosmological N-body simulations, we compute derivatives of ΔΣ, w_p,cg, and w_p,gg with respect to σ₈, Ω_m, σ _{ln M_ c}, 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 ΔΣ, 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 ≈ 2 × 10¹⁴ h^-1 M_⊙, we forecast a 1.4 per cent constraint on σ₈ while marginalizing over σ _{ln M_ c} and all HOD parameters. Reducing the mass threshold to 1 × 10¹⁴ h^-1 M_⊙ 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 ΔΣ have comparable constraining power, allowing internal consistency tests from such an analysis.