Cosmological Constraints from the Red-Sequence Cluster Survey

[abridged] We present a first cosmological analysis of a refined cluster catalog from the Red-Sequence Cluster Survey (RCS). The input cluster sample is derived from 72.07 square degrees of imaging data [...] The catalog contains 956 clusters over 0.35<z<0.95, limited by cluster richness and richness error. The calibration of the survey images has been extensively cross-checked against publicly available Sloan Digital Sky Survey imaging [...] We analyze the cluster sample via a general self-calibration technique including scatter in the mass-richness relation [...]. We fit simultaneously for Omega_M and sigma_8, and four parameters describing the calibration of cluster richness to mass, its evolution with redshift, and scatter in the richness-mass relation. The principal goal of this general analysis is to establish the consistency (or lack thereof) between the fitted parameters (both cosmological and cluster mass observables) and available results on both from independent measures. From an unconstrained analysis, Omega_M and sigma_8 are 0.31+0.11-0.10 and 0.67+0.18-0.13 respectively. An analysis including Gaussian priors on the slope and zeropoint of the mass-richness relation gives very similar results: 0.30+0.12-0.11 and 0.70+0.27-0.15. Both analyses are in good agreement with the current literature. The parameters describing the mass-richness relation in the unconstrained fit are also eminently reasonable and agree with existing follow-up data on both the RCS-1 and other cluster samples. Our results directly demonstrate that future surveys (optical and otherwise), with much larger samples of clusters, can give constraints competitive with other probes of cosmology.