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.
