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

We forecast constraints on the amplitude of matter clustering sigma_8(z) achievable with combination cluster weak lensing and number counts, in current next-generation surveys. advocate an approach, analogous to galaxy-galaxy lensing, which observables each redshift bin are mean counts profile clusters above a mass proxy threshold. The primary astrophysical nuisance parameter is logarithmic scatter between true near For surveys similar Dark Energy Survey (DES), Roman Space Telescope High Latitude (HLS), Rubin Observatory Legacy Time (LSST), we aggregate precision sigma_8 0.26%, 0.24%, 0.10%, respectively, if mass-observable has external prior better than 0.01. These would be degraded by about 20% for 0.05 case DES or HLS 0.016 LSST. A one-month observing program targeting approximately 2500 massive could achieve 0.5% constraint sigma_8(z=0.7) its own, ~0.33% HLS. Realizing constraining power requires accurate knowledge relation stringent control systematics. provide analytic approximations our numerical results that allow easy scaling other survey assumptions methods estimation.