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

We perform the first blind analysis of cluster abundance data. Specifically, we derive cosmological constraints from the abundance and weak-lensing signal of \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). We simultaneously fit for cosmological parameters and the richness--mass relation of the clusters. For a flat $\Lambda$CDM cosmological model with massive neutrinos, we find $S_8 \equiv \sigma_{8}(\Omega_m/0.3)^{0.5}=0.79^{+0.05}_{-0.04}$. This value is both consistent and competitive with that derived from cluster catalogues selected in different wavelengths. Our result is also consistent with the combined probes analyses by the Dark Energy Survey (DES) and the Kilo-Degree Survey (KiDS), and with the Cosmic Microwave Background (CMB) anisotropies as measured by \planck. We demonstrate that the cosmological posteriors are robust against variation of the richness--mass relation model and to systematics associated with the calibration of the selection function. In combination with Baryon Acoustic Oscillation (BAO) data and Big-Bang Nucleosynthesis (BBN) data, we constrain 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 the richness--mass relation has the potential to significantly improve the precision of our cosmological posteriors. The methods described in this work were developed for use in the forthcoming analysis of cluster abundances in the DES. Our SDSS analysis constitutes the first part of a staged-unblinding analysis of the full DES data set.