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We perform the first blind analysis of cluster abundance data. Specifically,we derive cosmological constraints from the abundance and weak-lensing signalof \redmapper\ clusters of richness $\lambda\geq 20$ in the redshift range$z\in[0.1,0.3]$ as measured in the Sloan Digital Sky Survey (SDSS). Wesimultaneously fit for cosmological parameters and the richness--mass relationof the clusters. For a flat $\Lambda$CDM cosmological model with massiveneutrinos, we find $S_8 \equiv\sigma_{8}(\Omega_m/0.3)^{0.5}=0.79^{+0.05}_{-0.04}$. This value is bothconsistent and competitive with that derived from cluster catalogues selectedin different wavelengths. Our result is also consistent with the combinedprobes analyses by the Dark Energy Survey (DES) and the Kilo-Degree Survey(KiDS), and with the Cosmic Microwave Background (CMB) anisotropies as measuredby \planck. We demonstrate that the cosmological posteriors are robust againstvariation of the richness--mass relation model and to systematics associatedwith the calibration of the selection function. In combination with BaryonAcoustic Oscillation (BAO) data and Big-Bang Nucleosynthesis (BBN) data, weconstrain the Hubble rate to be $h=0.66\pm 0.02$, independent of the CMB.Future work aimed at improving our understanding of the scatter of therichness--mass relation has the potential to significantly improve theprecision of our cosmological posteriors. The methods described in this workwere developed for use in the forthcoming analysis of cluster abundances in theDES. Our SDSS analysis constitutes the first part of a staged-unblindinganalysis of the full DES data set.

Dark Energy Survey Year 1 Results: Methods for Cluster Cosmology and Application to the SDSS