Cosmology with Galaxy Cluster Weak Lensing: Statistical Limits and Experimental Design

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We forecast constraints on the amplitude of matter clustering σM8(z) achievable with the combination of cluster weak lensing and number counts, in current and next-generation weak lensing surveys. We advocate for an approach, analogous to galaxy–galaxy lensing, in which the observables in each redshift bin are the mean number counts and the mean weak lensing profile of clusters above a mass proxy threshold. The primary astrophysical nuisance parameter is the logarithmic scatter σlnM between the mass proxy and true mass near the threshold. For surveys similar to the Dark Energy Survey (DES), the Roman Space Telescope High Latitude Survey (HLS), and the Rubin Observatory Legacy Survey of Space and Time (LSST), we forecast aggregate precision on σ8 of 0.26%, 0.24%, and 0.10%, respectively, if the mass–observable scatter is known externally to ΔσlnM ≤ 0.01. These constraints would be degraded by about 20% for ΔσlnM = 0.05. in the case of DES or HLS and for ΔσlnM = 0.016 for LSST. A 1 month observing program with Roman Space Telescope targeting ∼2500 massive clusters could achieve a ∼ 0.5% constraint on σ8(z = 0.7) on its own, or a ∼ 0.33% constraint in combination with the HLS. Realizing the constraining power of clusters Requires accurate knowledge of the mass–observable relation and stringent control of systematics. We provide analytic approximations to our numerical results that allow for easy scaling to other survey assumptions or other methods of cluster mass estimation.